diff --git "a/parse/train/HyPpD0g0Z/HyPpD0g0Z_middle.json" "b/parse/train/HyPpD0g0Z/HyPpD0g0Z_middle.json" new file mode 100644--- /dev/null +++ "b/parse/train/HyPpD0g0Z/HyPpD0g0Z_middle.json" @@ -0,0 +1,73944 @@ +{ + "pdf_info": [ + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 78, + 503, + 116 + ], + "lines": [ + { + "bbox": [ + 106, + 77, + 505, + 98 + ], + "spans": [ + { + "bbox": [ + 106, + 77, + 505, + 98 + ], + "score": 1.0, + "content": "GROUPING-BY-ID: GUARDING AGAINST ADVERSAR-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 99, + 260, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 99, + 260, + 118 + ], + "score": 1.0, + "content": "IAL DOMAIN SHIFTS", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 112, + 136, + 244, + 157 + ], + "lines": [ + { + "bbox": [ + 113, + 136, + 201, + 147 + ], + "spans": [ + { + "bbox": [ + 113, + 136, + 201, + 147 + ], + "score": 1.0, + "content": "Anonymous authors", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 112, + 146, + 245, + 159 + ], + "spans": [ + { + "bbox": [ + 112, + 146, + 245, + 159 + ], + "score": 1.0, + "content": "Paper under double-blind review", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 278, + 187, + 333, + 199 + ], + "lines": [ + { + "bbox": [ + 276, + 186, + 335, + 200 + ], + "spans": [ + { + "bbox": [ + 276, + 186, + 335, + 200 + ], + "score": 1.0, + "content": "ABSTRACT", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 143, + 213, + 468, + 366 + ], + "lines": [ + { + "bbox": [ + 142, + 213, + 469, + 226 + ], + "spans": [ + { + "bbox": [ + 142, + 213, + 469, + 226 + ], + "score": 1.0, + "content": "When training a deep neural network for supervised image classification, one can", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 141, + 224, + 469, + 237 + ], + "spans": [ + { + "bbox": [ + 141, + 224, + 469, + 237 + ], + "score": 1.0, + "content": "broadly distinguish between two types of latent features of images that will drive", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 141, + 235, + 469, + 248 + ], + "spans": [ + { + "bbox": [ + 141, + 235, + 244, + 248 + ], + "score": 1.0, + "content": "the classification of class", + "type": "text" + }, + { + "bbox": [ + 244, + 235, + 253, + 245 + ], + "score": 0.73, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 235, + 469, + 248 + ], + "score": 1.0, + "content": ". 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These latter orthogonal features would", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 290, + 470, + 302 + ], + "spans": [ + { + "bbox": [ + 141, + 290, + 470, + 302 + ], + "score": 1.0, + "content": "generally include features such as position, rotation, image quality or brightness", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 300, + 470, + 314 + ], + "spans": [ + { + "bbox": [ + 141, + 300, + 470, + 314 + ], + "score": 1.0, + "content": "but also more complex ones like hair color or posture for images of persons. We", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 312, + 470, + 325 + ], + "spans": [ + { + "bbox": [ + 141, + 312, + 470, + 325 + ], + "score": 1.0, + "content": "try to guard against future adversarial domain shifts by ideally just using the ‘con-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 142, + 323, + 469, + 335 + ], + "spans": [ + { + "bbox": [ + 142, + 323, + 469, + 335 + ], + "score": 1.0, + "content": "ditionally invariant’ features for classification. In contrast to previous work, we", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 334, + 470, + 346 + ], + "spans": [ + { + "bbox": [ + 141, + 334, + 470, + 346 + ], + "score": 1.0, + "content": "assume that the domain itself is not observed and hence a latent variable. We", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 345, + 470, + 357 + ], + "spans": [ + { + "bbox": [ + 141, + 345, + 470, + 357 + ], + "score": 1.0, + "content": "can hence not directly see the distributional change of features across different", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 142, + 356, + 181, + 367 + ], + "spans": [ + { + "bbox": [ + 142, + 356, + 181, + 367 + ], + "score": 1.0, + "content": "domains.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 11.5, + "bbox_fs": [ + 141, + 213, + 470, + 367 + ] + }, + { + "type": "text", + "bbox": [ + 142, + 370, + 468, + 435 + ], + "lines": [ + { + "bbox": [ + 142, + 370, + 469, + 381 + ], + "spans": [ + { + "bbox": [ + 142, + 370, + 469, + 381 + ], + "score": 1.0, + "content": "We do assume, however, that we can sometimes observe a so-called identifier or", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 380, + 469, + 393 + ], + "spans": [ + { + "bbox": [ + 141, + 380, + 469, + 393 + ], + "score": 1.0, + "content": "ID variable. We might know, for example, that two images show the same person,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 392, + 470, + 405 + ], + "spans": [ + { + "bbox": [ + 141, + 392, + 470, + 405 + ], + "score": 1.0, + "content": "with ID referring to the identity of the person. In data augmentation, we generate", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 402, + 470, + 416 + ], + "spans": [ + { + "bbox": [ + 141, + 402, + 470, + 416 + ], + "score": 1.0, + "content": "several images from the same original image, with ID referring to the relevant", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 414, + 470, + 427 + ], + "spans": [ + { + "bbox": [ + 141, + 414, + 470, + 427 + ], + "score": 1.0, + "content": "original image. The method requires only a small fraction of images to have an", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 424, + 193, + 436 + ], + "spans": [ + { + "bbox": [ + 141, + 424, + 193, + 436 + ], + "score": 1.0, + "content": "ID variable.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5, + "bbox_fs": [ + 141, + 370, + 470, + 436 + ] + }, + { + "type": "text", + "bbox": [ + 143, + 439, + 468, + 570 + ], + "lines": [ + { + "bbox": [ + 142, + 438, + 469, + 451 + ], + "spans": [ + { + "bbox": [ + 142, + 438, + 469, + 451 + ], + "score": 1.0, + "content": "We provide a causal framework for the problem by adding the ID variable to the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 142, + 450, + 469, + 461 + ], + "spans": [ + { + "bbox": [ + 142, + 450, + 469, + 461 + ], + "score": 1.0, + "content": "model of Gong et al. (2016). However, we are interested in settings where we", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 141, + 461, + 470, + 472 + ], + "spans": [ + { + "bbox": [ + 141, + 461, + 470, + 472 + ], + "score": 1.0, + "content": "cannot observe the domain directly and we treat domain as a latent variable. If", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 141, + 471, + 470, + 483 + ], + "spans": [ + { + "bbox": [ + 141, + 471, + 374, + 483 + ], + "score": 1.0, + "content": "two or more samples share the same class and identifier,", + "type": "text" + }, + { + "bbox": [ + 374, + 471, + 445, + 483 + ], + "score": 0.93, + "content": "( Y , \\mathrm { I D } ) = ( y , \\mathrm { i d } )", + "type": "inline_equation" + }, + { + "bbox": [ + 445, + 471, + 470, + 483 + ], + "score": 1.0, + "content": ", then", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 141, + 483, + 469, + 494 + ], + "spans": [ + { + "bbox": [ + 141, + 483, + 469, + 494 + ], + "score": 1.0, + "content": "we treat those samples as counterfactuals under different style interventions on the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 141, + 493, + 470, + 506 + ], + "spans": [ + { + "bbox": [ + 141, + 493, + 470, + 506 + ], + "score": 1.0, + "content": "orthogonal or style features. Using this grouping-by-ID approach, we regularize", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 141, + 504, + 470, + 517 + ], + "spans": [ + { + "bbox": [ + 141, + 504, + 470, + 517 + ], + "score": 1.0, + "content": "the network to provide near constant output across samples that share the same", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 141, + 515, + 470, + 528 + ], + "spans": [ + { + "bbox": [ + 141, + 515, + 470, + 528 + ], + "score": 1.0, + "content": "ID by penalizing with an appropriate graph Laplacian. This is shown to substan-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 141, + 526, + 469, + 540 + ], + "spans": [ + { + "bbox": [ + 141, + 526, + 469, + 540 + ], + "score": 1.0, + "content": "tially improve performance in settings where domains change in terms of image", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 141, + 538, + 470, + 550 + ], + "spans": [ + { + "bbox": [ + 141, + 538, + 470, + 550 + ], + "score": 1.0, + "content": "quality, brightness, color changes, and more complex changes such as changes in", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 141, + 548, + 469, + 561 + ], + "spans": [ + { + "bbox": [ + 141, + 548, + 469, + 561 + ], + "score": 1.0, + "content": "movement and posture. We show links to questions of interpretability, fairness", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 141, + 558, + 230, + 573 + ], + "spans": [ + { + "bbox": [ + 141, + 558, + 230, + 573 + ], + "score": 1.0, + "content": "and transfer learning.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30.5, + "bbox_fs": [ + 141, + 438, + 470, + 573 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 596, + 206, + 608 + ], + "lines": [ + { + "bbox": [ + 105, + 594, + 208, + 611 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 208, + 611 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 622, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "score": 1.0, + "content": "Deep neural networks (DNNs) have achieved outstanding performance on prediction tasks like vi-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "score": 1.0, + "content": "sual object and speech recognition (Krizhevsky et al., 2012; Szegedy et al., 2015; He et al., 2015).", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "Issues can arise when the learned representations rely on dependencies that vanish in test distribu-", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 653, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 505, + 669 + ], + "score": 1.0, + "content": "tions (e.g. see Csurka (2017) and references therein). Such domain shifts can be caused by changing", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "conditions, e.g. color, background or location changes arising when deploying the machine learn-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "score": 1.0, + "content": "ing (ML) system in production. Predictive performance is then likely to degrade. For instance, the", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "“Russian tank legend” is an example where the training data was subject to sampling biases that", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "were not replicated in the real world. Concretely, the story relates how a machine learning system", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "was trained to distinguish between Russian and American tanks from photos. The accuracy was very", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 721, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 506, + 733 + ], + "score": 1.0, + "content": "high but only due to the fact that all images of Russian tanks were of bad quality while the photos of", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 42.5, + "bbox_fs": [ + 105, + 621, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "American tanks were not. The system learned to discriminate between images of different qualities", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 335, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 335, + 106 + ], + "score": 1.0, + "content": "but would have failed badly in practice (Emspak, 2016)1.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 106, + 111, + 505, + 253 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "Hidden confounding factors like in the example above between image quality and the origin of the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 121, + 505, + 135 + ], + "spans": [ + { + "bbox": [ + 105, + 121, + 505, + 135 + ], + "score": 1.0, + "content": "tank give rise to indirect associations. These are arguably one reason why deep learning requires", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "score": 1.0, + "content": "large sample sizes as large sample sizes tend to ensure that the effect of the confounding factors", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 142, + 505, + 157 + ], + "spans": [ + { + "bbox": [ + 104, + 142, + 505, + 157 + ], + "score": 1.0, + "content": "averages out (although a large sample size is clearly not per se a guarantee that the confounding", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 154, + 506, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 506, + 167 + ], + "score": 1.0, + "content": "effect will become weaker). A large sample size is also required if one is trying to achieve invariance", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "score": 1.0, + "content": "to known factors like translation, point of view, and rotation by using data augmentation. Another", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "related example where human and artificial cognition deviate strongly are adversarial examples—", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "score": 1.0, + "content": "imperceptibly but intentionally perturbed inputs that are misclassified by a ML model (Szegedy", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "score": 1.0, + "content": "et al., 2014; Goodfellow et al., 2015). Adversarial examples do not fool humans and in general we", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "only need to see one rotated example of the same object to achieve invariance to rotations in our", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 220, + 506, + 234 + ], + "spans": [ + { + "bbox": [ + 104, + 220, + 506, + 234 + ], + "score": 1.0, + "content": "perception. Our starting point is the question whether we can in a simple way mimic the human", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 505, + 244 + ], + "score": 1.0, + "content": "ability to learn desired invariances from a few instances of the same object and whether we can", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 241, + 353, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 353, + 255 + ], + "score": 1.0, + "content": "better align the features DNNs exploit with human cognition.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 259, + 505, + 358 + ], + "lines": [ + { + "bbox": [ + 106, + 258, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 106, + 258, + 505, + 271 + ], + "score": 1.0, + "content": "Considerations of fairness and discrimination might be another reason why we are interested in", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 270, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 505, + 282 + ], + "score": 1.0, + "content": "controlling that certain characteristics of the input data are not included in the learned representations", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 281, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 505, + 293 + ], + "score": 1.0, + "content": "and thus have no impact on the resulting decisions (Barocas & Selbst, 2016; Kilbertus et al., 2017).", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 292, + 505, + 303 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 505, + 303 + ], + "score": 1.0, + "content": "Unfortunately, existing biases in datasets used for training ML algorithms tend to be replicated in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 302, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 506, + 316 + ], + "score": 1.0, + "content": "the estimated models (Bolukbasi et al., 2016). For instance, in June 2015 Google’s photo app tagged", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "score": 1.0, + "content": "two non-white people as “gorillas”—most likely because the training examples for “people” were", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 325, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 505, + 338 + ], + "score": 1.0, + "content": "mainly photos of white persons, making “color” predictive for the class label (Crawford, 2016;", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "score": 1.0, + "content": "Emspak, 2016). A human would not make the same mistake after only seeing one instance of a", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 347, + 180, + 359 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 180, + 359 + ], + "score": 1.0, + "content": "non-white person.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 363, + 505, + 484 + ], + "lines": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "score": 1.0, + "content": "Addressing the issues outlined above, we propose counterfactual regularization (CORE) to control", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 374, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 505, + 387 + ], + "score": 1.0, + "content": "what latent features an estimator extracts from the input data. Conceptually, we take a causal view", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "score": 1.0, + "content": "of the data generating process and categorize the latent data generating factors into ‘conditionally", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 396, + 507, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 507, + 410 + ], + "score": 1.0, + "content": "invariant’ (core) and ‘orthogonal’ (style) features, as in (Gong et al., 2016). It is desirable that a", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "classifier uses only the core features as they pertain to the target of interest in a stable and coherent", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 417, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 104, + 417, + 506, + 432 + ], + "score": 1.0, + "content": "fashion. CORE yields an estimator which is invariant to factors of variation corresponding to style", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "features. Consequently, it is robust with respect to adversarial domain shifts, arising through arbi-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 441, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 505, + 452 + ], + "score": 1.0, + "content": "trarily strong interventions on the style features. CORE relies on the fact that for certain datasets", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 451, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 505, + 464 + ], + "score": 1.0, + "content": "we can observe “counterfactuals” in the sense that we observe the same object under different con-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "ditions. Rather than pooling over all examples, CORE exploits knowledge about this grouping, i.e.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 473, + 315, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 315, + 485 + ], + "score": 1.0, + "content": "that a number of instances relate to the same object.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 490, + 504, + 545 + ], + "lines": [ + { + "bbox": [ + 106, + 489, + 506, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 342, + 503 + ], + "score": 1.0, + "content": "The remainder of this manuscript is structured as follows:", + "type": "text" + }, + { + "bbox": [ + 343, + 490, + 354, + 501 + ], + "score": 0.74, + "content": "\\ S 2", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 489, + 506, + 503 + ], + "score": 1.0, + "content": "starts with two motivating examples,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 500, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 506, + 514 + ], + "score": 1.0, + "content": "showing how CORE can reduce the need for data augmentation and help predictive performance in", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 512, + 505, + 525 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 224, + 525 + ], + "score": 1.0, + "content": "small sample size settings. In", + "type": "text" + }, + { + "bbox": [ + 225, + 512, + 235, + 523 + ], + "score": 0.61, + "content": "\\ S 3", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 512, + 356, + 525 + ], + "score": 1.0, + "content": "we review related work and in", + "type": "text" + }, + { + "bbox": [ + 356, + 512, + 367, + 523 + ], + "score": 0.57, + "content": "\\ S 4", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 512, + 505, + 525 + ], + "score": 1.0, + "content": "we formally introduce counterfac-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 522, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 536 + ], + "score": 1.0, + "content": "tual regularization, along with the CORE estimator and theoretical insights for the logistic regression", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 534, + 458, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 458, + 547 + ], + "score": 1.0, + "content": "setting. In §5 we further evaluate the performance of CORE in a variety of experiments.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37 + }, + { + "type": "title", + "bbox": [ + 109, + 563, + 276, + 576 + ], + "lines": [ + { + "bbox": [ + 105, + 561, + 278, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 278, + 578 + ], + "score": 1.0, + "content": "2 TWO MOTIVATING EXAMPLES", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 105, + 590, + 470, + 600 + ], + "lines": [ + { + "bbox": [ + 106, + 588, + 471, + 602 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 471, + 602 + ], + "score": 1.0, + "content": "2.1 GROUPING PHOTOS OF THE SAME PERSON: BETTER PREDICTIVE PERFORMANCE", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 107, + 610, + 505, + 699 + ], + "lines": [ + { + "bbox": [ + 106, + 610, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 610, + 506, + 623 + ], + "score": 1.0, + "content": "The CelebA dataset (Liu et al., 2015) contains face images of celebrities. We consider the task of", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "score": 1.0, + "content": "classifying whether a person wears glasses. Several photos of the same person are available. We use", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "this grouping information and constrain the classification to yield the same prediction for all images", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "belonging to the same person and sharing the same class label. We call the additional instances", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "of the same person counterfactual (CF) observations. Figure 1a shows examples from the training", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "set. The standard approach would be to pool all examples. The only additional information we", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 357, + 689 + ], + "score": 1.0, + "content": "exploit is that some observations can be grouped. We include", + "type": "text" + }, + { + "bbox": [ + 357, + 677, + 389, + 687 + ], + "score": 0.9, + "content": "n = 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "identities in the training set,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 235, + 700 + ], + "score": 1.0, + "content": "resulting in a total sample size", + "type": "text" + }, + { + "bbox": [ + 236, + 687, + 277, + 698 + ], + "score": 0.9, + "content": "m = 3 2 1", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "as there are approximately 30 images of each person2.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 45.5 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 118, + 710, + 399, + 732 + ], + "lines": [ + { + "bbox": [ + 119, + 709, + 368, + 722 + ], + "spans": [ + { + "bbox": [ + 119, + 709, + 368, + 722 + ], + "score": 1.0, + "content": "1A different version of this story can be found in Yudkowsky (2008).", + "type": "text" + } + ] + }, + { + "bbox": [ + 118, + 720, + 401, + 733 + ], + "spans": [ + { + "bbox": [ + 118, + 720, + 201, + 733 + ], + "score": 1.0, + "content": "2Additional results for", + "type": "text" + }, + { + "bbox": [ + 202, + 723, + 209, + 730 + ], + "score": 0.73, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 209, + 720, + 401, + 733 + ], + "score": 1.0, + "content": "ranging from 10 to 160 can be found in Figure C.7b.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 26, + 309, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 26, + 309, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 13, + "width": 8 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "American tanks were not. The system learned to discriminate between images of different qualities", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 335, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 335, + 106 + ], + "score": 1.0, + "content": "but would have failed badly in practice (Emspak, 2016)1.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5, + "bbox_fs": [ + 105, + 82, + 505, + 106 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 111, + 505, + 253 + ], + "lines": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "Hidden confounding factors like in the example above between image quality and the origin of the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 121, + 505, + 135 + ], + "spans": [ + { + "bbox": [ + 105, + 121, + 505, + 135 + ], + "score": 1.0, + "content": "tank give rise to indirect associations. These are arguably one reason why deep learning requires", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 505, + 145 + ], + "score": 1.0, + "content": "large sample sizes as large sample sizes tend to ensure that the effect of the confounding factors", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 104, + 142, + 505, + 157 + ], + "spans": [ + { + "bbox": [ + 104, + 142, + 505, + 157 + ], + "score": 1.0, + "content": "averages out (although a large sample size is clearly not per se a guarantee that the confounding", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 154, + 506, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 506, + 167 + ], + "score": 1.0, + "content": "effect will become weaker). A large sample size is also required if one is trying to achieve invariance", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "score": 1.0, + "content": "to known factors like translation, point of view, and rotation by using data augmentation. Another", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "related example where human and artificial cognition deviate strongly are adversarial examples—", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "score": 1.0, + "content": "imperceptibly but intentionally perturbed inputs that are misclassified by a ML model (Szegedy", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 211 + ], + "score": 1.0, + "content": "et al., 2014; Goodfellow et al., 2015). Adversarial examples do not fool humans and in general we", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "only need to see one rotated example of the same object to achieve invariance to rotations in our", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 220, + 506, + 234 + ], + "spans": [ + { + "bbox": [ + 104, + 220, + 506, + 234 + ], + "score": 1.0, + "content": "perception. Our starting point is the question whether we can in a simple way mimic the human", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 505, + 244 + ], + "score": 1.0, + "content": "ability to learn desired invariances from a few instances of the same object and whether we can", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 241, + 353, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 353, + 255 + ], + "score": 1.0, + "content": "better align the features DNNs exploit with human cognition.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 8, + "bbox_fs": [ + 104, + 110, + 506, + 255 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 259, + 505, + 358 + ], + "lines": [ + { + "bbox": [ + 106, + 258, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 106, + 258, + 505, + 271 + ], + "score": 1.0, + "content": "Considerations of fairness and discrimination might be another reason why we are interested in", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 270, + 505, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 270, + 505, + 282 + ], + "score": 1.0, + "content": "controlling that certain characteristics of the input data are not included in the learned representations", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 281, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 505, + 293 + ], + "score": 1.0, + "content": "and thus have no impact on the resulting decisions (Barocas & Selbst, 2016; Kilbertus et al., 2017).", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 292, + 505, + 303 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 505, + 303 + ], + "score": 1.0, + "content": "Unfortunately, existing biases in datasets used for training ML algorithms tend to be replicated in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 302, + 506, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 506, + 316 + ], + "score": 1.0, + "content": "the estimated models (Bolukbasi et al., 2016). For instance, in June 2015 Google’s photo app tagged", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "score": 1.0, + "content": "two non-white people as “gorillas”—most likely because the training examples for “people” were", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 325, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 505, + 338 + ], + "score": 1.0, + "content": "mainly photos of white persons, making “color” predictive for the class label (Crawford, 2016;", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "score": 1.0, + "content": "Emspak, 2016). A human would not make the same mistake after only seeing one instance of a", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 347, + 180, + 359 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 180, + 359 + ], + "score": 1.0, + "content": "non-white person.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19, + "bbox_fs": [ + 105, + 258, + 506, + 359 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 363, + 505, + 484 + ], + "lines": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 363, + 505, + 376 + ], + "score": 1.0, + "content": "Addressing the issues outlined above, we propose counterfactual regularization (CORE) to control", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 374, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 505, + 387 + ], + "score": 1.0, + "content": "what latent features an estimator extracts from the input data. Conceptually, we take a causal view", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 398 + ], + "score": 1.0, + "content": "of the data generating process and categorize the latent data generating factors into ‘conditionally", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 396, + 507, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 507, + 410 + ], + "score": 1.0, + "content": "invariant’ (core) and ‘orthogonal’ (style) features, as in (Gong et al., 2016). It is desirable that a", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 506, + 420 + ], + "score": 1.0, + "content": "classifier uses only the core features as they pertain to the target of interest in a stable and coherent", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 104, + 417, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 104, + 417, + 506, + 432 + ], + "score": 1.0, + "content": "fashion. CORE yields an estimator which is invariant to factors of variation corresponding to style", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "features. Consequently, it is robust with respect to adversarial domain shifts, arising through arbi-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 441, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 505, + 452 + ], + "score": 1.0, + "content": "trarily strong interventions on the style features. CORE relies on the fact that for certain datasets", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 451, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 505, + 464 + ], + "score": 1.0, + "content": "we can observe “counterfactuals” in the sense that we observe the same object under different con-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "ditions. Rather than pooling over all examples, CORE exploits knowledge about this grouping, i.e.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 473, + 315, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 315, + 485 + ], + "score": 1.0, + "content": "that a number of instances relate to the same object.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 29, + "bbox_fs": [ + 104, + 363, + 507, + 485 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 490, + 504, + 545 + ], + "lines": [ + { + "bbox": [ + 106, + 489, + 506, + 503 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 342, + 503 + ], + "score": 1.0, + "content": "The remainder of this manuscript is structured as follows:", + "type": "text" + }, + { + "bbox": [ + 343, + 490, + 354, + 501 + ], + "score": 0.74, + "content": "\\ S 2", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 489, + 506, + 503 + ], + "score": 1.0, + "content": "starts with two motivating examples,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 500, + 506, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 506, + 514 + ], + "score": 1.0, + "content": "showing how CORE can reduce the need for data augmentation and help predictive performance in", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 512, + 505, + 525 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 224, + 525 + ], + "score": 1.0, + "content": "small sample size settings. In", + "type": "text" + }, + { + "bbox": [ + 225, + 512, + 235, + 523 + ], + "score": 0.61, + "content": "\\ S 3", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 512, + 356, + 525 + ], + "score": 1.0, + "content": "we review related work and in", + "type": "text" + }, + { + "bbox": [ + 356, + 512, + 367, + 523 + ], + "score": 0.57, + "content": "\\ S 4", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 512, + 505, + 525 + ], + "score": 1.0, + "content": "we formally introduce counterfac-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 522, + 506, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 536 + ], + "score": 1.0, + "content": "tual regularization, along with the CORE estimator and theoretical insights for the logistic regression", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 534, + 458, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 458, + 547 + ], + "score": 1.0, + "content": "setting. In §5 we further evaluate the performance of CORE in a variety of experiments.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 489, + 506, + 547 + ] + }, + { + "type": "title", + "bbox": [ + 109, + 563, + 276, + 576 + ], + "lines": [ + { + "bbox": [ + 105, + 561, + 278, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 278, + 578 + ], + "score": 1.0, + "content": "2 TWO MOTIVATING EXAMPLES", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 105, + 590, + 470, + 600 + ], + "lines": [ + { + "bbox": [ + 106, + 588, + 471, + 602 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 471, + 602 + ], + "score": 1.0, + "content": "2.1 GROUPING PHOTOS OF THE SAME PERSON: BETTER PREDICTIVE PERFORMANCE", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 41, + "bbox_fs": [ + 106, + 588, + 471, + 602 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 610, + 505, + 699 + ], + "lines": [ + { + "bbox": [ + 106, + 610, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 610, + 506, + 623 + ], + "score": 1.0, + "content": "The CelebA dataset (Liu et al., 2015) contains face images of celebrities. We consider the task of", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 635 + ], + "score": 1.0, + "content": "classifying whether a person wears glasses. Several photos of the same person are available. We use", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "this grouping information and constrain the classification to yield the same prediction for all images", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "belonging to the same person and sharing the same class label. We call the additional instances", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "of the same person counterfactual (CF) observations. Figure 1a shows examples from the training", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 506, + 678 + ], + "score": 1.0, + "content": "set. The standard approach would be to pool all examples. The only additional information we", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 357, + 689 + ], + "score": 1.0, + "content": "exploit is that some observations can be grouped. We include", + "type": "text" + }, + { + "bbox": [ + 357, + 677, + 389, + 687 + ], + "score": 0.9, + "content": "n = 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 389, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "identities in the training set,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 235, + 700 + ], + "score": 1.0, + "content": "resulting in a total sample size", + "type": "text" + }, + { + "bbox": [ + 236, + 687, + 277, + 698 + ], + "score": 0.9, + "content": "m = 3 2 1", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "as there are approximately 30 images of each person2.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 45.5, + "bbox_fs": [ + 105, + 610, + 506, + 700 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 137, + 81, + 276, + 91 + ], + "lines": [ + { + "bbox": [ + 136, + 79, + 276, + 93 + ], + "spans": [ + { + "bbox": [ + 136, + 79, + 276, + 93 + ], + "score": 1.0, + "content": "(a) Grouping-by-ID with ID=identity.", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 325, + 81, + 488, + 91 + ], + "lines": [ + { + "bbox": [ + 324, + 79, + 489, + 93 + ], + "spans": [ + { + "bbox": [ + 324, + 79, + 427, + 93 + ], + "score": 1.0, + "content": "(b) Grouping-by-ID with ID", + "type": "text" + }, + { + "bbox": [ + 428, + 82, + 434, + 90 + ], + "score": 0.35, + "content": "=", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 79, + 489, + 93 + ], + "score": 1.0, + "content": "original image.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "image", + "bbox": [ + 117, + 94, + 502, + 200 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 117, + 94, + 502, + 200 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 117, + 94, + 502, + 200 + ], + "spans": [ + { + "bbox": [ + 117, + 94, + 502, + 200 + ], + "score": 0.953, + "type": "image", + "image_path": "ba66922606a44436f08eff197b11fa3c0dbae95f221a2936a7176b3141d60bbd.jpg" + } + ] + } + ], + "index": 3, + "virtual_lines": [ + { + "bbox": [ + 117, + 94, + 502, + 129.33333333333334 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 117, + 129.33333333333334, + 502, + 164.66666666666669 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 117, + 164.66666666666669, + 502, + 200.00000000000003 + ], + "spans": [], + "index": 4 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 204, + 505, + 264 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 204, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 505, + 216 + ], + "score": 1.0, + "content": "Figure 1: Examples from a) the subsampled CelebA dataset and b) the augmented MNIST dataset. Connected", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 215, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 505, + 225 + ], + "score": 1.0, + "content": "images are counterfactual examples as they share the same realization of the ID which is the identity of the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 224, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 224, + 505, + 236 + ], + "score": 1.0, + "content": "person in a) and the original image used for data augmentation in b). The comparison is a training of exactly", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 233, + 505, + 246 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 505, + 246 + ], + "score": 1.0, + "content": "the same network architecture that does not make use of the grouping information but using a standard ridge", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 244, + 506, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 379, + 256 + ], + "score": 1.0, + "content": "penalty. In a) exploiting the grouping information reduces the test error by", + "type": "text" + }, + { + "bbox": [ + 379, + 244, + 397, + 254 + ], + "score": 0.86, + "content": "32 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 397, + 244, + 506, + 256 + ], + "score": 1.0, + "content": "compared to pooling over all", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 254, + 339, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 318, + 266 + ], + "score": 1.0, + "content": "samples. In b) the test error on rotated digits is reduced by", + "type": "text" + }, + { + "bbox": [ + 318, + 254, + 335, + 264 + ], + "score": 0.88, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 254, + 339, + 266 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 7.5 + } + ], + "index": 5.25 + }, + { + "type": "text", + "bbox": [ + 108, + 281, + 504, + 314 + ], + "lines": [ + { + "bbox": [ + 105, + 280, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 367, + 294 + ], + "score": 1.0, + "content": "Exploiting the group structure reduces the average test error from", + "type": "text" + }, + { + "bbox": [ + 367, + 281, + 399, + 291 + ], + "score": 0.86, + "content": "2 4 . 7 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 280, + 410, + 294 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 411, + 281, + 442, + 291 + ], + "score": 0.87, + "content": "1 6 . 8 9 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 442, + 280, + 505, + 294 + ], + "score": 1.0, + "content": ", i.e. by approx.", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 290, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 126, + 302 + ], + "score": 0.85, + "content": "32 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 126, + 290, + 506, + 304 + ], + "score": 1.0, + "content": ", compared to the estimator which just pools all images and uses a standard ridge penalty for", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 301, + 172, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 172, + 315 + ], + "score": 1.0, + "content": "the cofficients3.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12 + }, + { + "type": "title", + "bbox": [ + 108, + 331, + 443, + 342 + ], + "lines": [ + { + "bbox": [ + 106, + 330, + 446, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 446, + 343 + ], + "score": 1.0, + "content": "2.2 GROUPING AUGMENTED IMAGES BY ORIGINAL: MORE SAMPLE EFFICIENT", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 352, + 505, + 495 + ], + "lines": [ + { + "bbox": [ + 105, + 352, + 505, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 505, + 366 + ], + "score": 1.0, + "content": "A different use case of CORE is to make data augmentation more efficient in terms of the required", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 362, + 505, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 505, + 378 + ], + "score": 1.0, + "content": "samples. In data augmentation, one creates additional samples by modifying the original inputs, e.g.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 375, + 506, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 506, + 388 + ], + "score": 1.0, + "content": "by rotating, translating, or flipping the images (Scholkopf et al., 1996). In other words, additional ¨", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 385, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 506, + 399 + ], + "score": 1.0, + "content": "samples are generated by interventions on style features. Using this augmented data set for training", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 397, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 505, + 410 + ], + "score": 1.0, + "content": "results in invariance of the estimator with respect to the transformations (style features) of interest.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 505, + 420 + ], + "score": 1.0, + "content": "For CORE we can use the grouping information that the original and the augmented samples belong", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 505, + 432 + ], + "score": 1.0, + "content": "to the same object. This enforces the invariance with respect to the style features more strongly", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "compared to normal data augmentation which just pools all samples. We assess this for the style", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 439, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 439, + 390, + 455 + ], + "score": 1.0, + "content": "feature “rotation” on MNIST (LeCun & Cortes, 2010) and only include", + "type": "text" + }, + { + "bbox": [ + 391, + 441, + 425, + 451 + ], + "score": 0.9, + "content": "c = 1 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 439, + 506, + 455 + ], + "score": 1.0, + "content": "augmented training", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 451, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 162, + 464 + ], + "score": 1.0, + "content": "examples for", + "type": "text" + }, + { + "bbox": [ + 163, + 452, + 212, + 462 + ], + "score": 0.89, + "content": "n = 1 0 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 212, + 451, + 428, + 464 + ], + "score": 1.0, + "content": "original samples, resulting in a total sample size of", + "type": "text" + }, + { + "bbox": [ + 428, + 452, + 480, + 462 + ], + "score": 0.88, + "content": "m = 1 0 1 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 451, + 506, + 464 + ], + "score": 1.0, + "content": ". The", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "degree of the rotations is sampled uniformly at random from [35, 70]. Figure 1b shows examples", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 473, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 486 + ], + "score": 1.0, + "content": "from the training set. By using CORE the average test error on rotated examples is reduced from", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 484, + 309, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 138, + 495 + ], + "score": 0.86, + "content": "3 2 . 8 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 139, + 484, + 150, + 497 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 150, + 484, + 182, + 495 + ], + "score": 0.86, + "content": "1 6 . 3 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 484, + 309, + 497 + ], + "score": 1.0, + "content": ", around half its original value4.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 21 + }, + { + "type": "title", + "bbox": [ + 108, + 515, + 209, + 528 + ], + "lines": [ + { + "bbox": [ + 105, + 514, + 210, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 210, + 530 + ], + "score": 1.0, + "content": "3 RELATED WORK", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 542, + 504, + 586 + ], + "lines": [ + { + "bbox": [ + 105, + 542, + 506, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 506, + 555 + ], + "score": 1.0, + "content": "Perhaps most similar to this work in terms of their goals are the work of Gong et al. (2016) and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 553, + 506, + 566 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 506, + 566 + ], + "score": 1.0, + "content": "Domain-Adversarial Neural Networks (DANN) proposed in Ganin et al. (2016), an approach moti-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 564, + 506, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 577 + ], + "score": 1.0, + "content": "vated by the work of Ben-David et al. (2007). While our approach requires grouped observations,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 575, + 423, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 423, + 587 + ], + "score": 1.0, + "content": "both of these works rely on unlabeled data from the target task being available.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5 + }, + { + "type": "text", + "bbox": [ + 107, + 592, + 504, + 647 + ], + "lines": [ + { + "bbox": [ + 105, + 591, + 506, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 506, + 605 + ], + "score": 1.0, + "content": "The main idea of Ganin et al. (2016) is to learn a representation that contains no discriminative", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 602, + 505, + 616 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 505, + 616 + ], + "score": 1.0, + "content": "information about the origin of the input (source or target domain). This is achieved by an adver-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 613, + 506, + 627 + ], + "spans": [ + { + "bbox": [ + 105, + 613, + 506, + 627 + ], + "score": 1.0, + "content": "sarial training procedure: the loss on domain classification is maximized while the loss of the target", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 624, + 506, + 638 + ], + "spans": [ + { + "bbox": [ + 105, + 624, + 506, + 638 + ], + "score": 1.0, + "content": "prediction task is minimized simultaneously. In contrast, we do not assume that we have data from", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 636, + 490, + 647 + ], + "spans": [ + { + "bbox": [ + 106, + 636, + 490, + 647 + ], + "score": 1.0, + "content": "different domains but just different realizations of the same object under different interventions.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 653, + 505, + 686 + ], + "lines": [ + { + "bbox": [ + 105, + 652, + 506, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 652, + 506, + 666 + ], + "score": 1.0, + "content": "The data generating process assumed in Gong et al. (2016) is similar to our model, introduced", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 104, + 663, + 506, + 677 + ], + "spans": [ + { + "bbox": [ + 104, + 663, + 117, + 677 + ], + "score": 1.0, + "content": "in", + "type": "text" + }, + { + "bbox": [ + 118, + 664, + 136, + 675 + ], + "score": 0.83, + "content": "\\ S 4 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 136, + 663, + 506, + 677 + ], + "score": 1.0, + "content": "where we detail the similarities and differences between the models (cf. Figure 2). Gong", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 675, + 504, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 504, + 687 + ], + "score": 1.0, + "content": "et al. (2016) identify the conditionally independent features by adjusting a transformation of the", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 39 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 700, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 698, + 505, + 713 + ], + "spans": [ + { + "bbox": [ + 118, + 698, + 505, + 713 + ], + "score": 1.0, + "content": "3Details on the architecture can be found in Table C.1. 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Connected", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 215, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 505, + 225 + ], + "score": 1.0, + "content": "images are counterfactual examples as they share the same realization of the ID which is the identity of the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 224, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 224, + 505, + 236 + ], + "score": 1.0, + "content": "person in a) and the original image used for data augmentation in b). The comparison is a training of exactly", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 233, + 505, + 246 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 505, + 246 + ], + "score": 1.0, + "content": "the same network architecture that does not make use of the grouping information but using a standard ridge", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 244, + 506, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 379, + 256 + ], + "score": 1.0, + "content": "penalty. 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This enforces the invariance with respect to the style features more strongly", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "compared to normal data augmentation which just pools all samples. 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The", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "degree of the rotations is sampled uniformly at random from [35, 70]. Figure 1b shows examples", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 473, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 486 + ], + "score": 1.0, + "content": "from the training set. By using CORE the average test error on rotated examples is reduced from", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 484, + 309, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 138, + 495 + ], + "score": 0.86, + "content": "3 2 . 8 6 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 139, + 484, + 150, + 497 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 150, + 484, + 182, + 495 + ], + "score": 0.86, + "content": "1 6 . 3 3 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 484, + 309, + 497 + ], + "score": 1.0, + "content": ", around half its original value4.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 352, + 506, + 497 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 515, + 209, + 528 + ], + "lines": [ + { + "bbox": [ + 105, + 514, + 210, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 210, + 530 + ], + "score": 1.0, + "content": "3 RELATED WORK", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 542, + 504, + 586 + ], + "lines": [ + { + "bbox": [ + 105, + 542, + 506, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 506, + 555 + ], + "score": 1.0, + "content": "Perhaps most similar to this work in terms of their goals are the work of Gong et al. (2016) and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 553, + 506, + 566 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 506, + 566 + ], + "score": 1.0, + "content": "Domain-Adversarial Neural Networks (DANN) proposed in Ganin et al. (2016), an approach moti-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 564, + 506, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 506, + 577 + ], + "score": 1.0, + "content": "vated by the work of Ben-David et al. (2007). While our approach requires grouped observations,", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 575, + 423, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 423, + 587 + ], + "score": 1.0, + "content": "both of these works rely on unlabeled data from the target task being available.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 542, + 506, + 587 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 592, + 504, + 647 + ], + "lines": [ + { + "bbox": [ + 105, + 591, + 506, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 506, + 605 + ], + "score": 1.0, + "content": "The main idea of Ganin et al. 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In contrast, we exploit", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 114, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 114, + 506, + 128 + ], + "score": 1.0, + "content": "presence of an identifier variable ID to penalize the classifier using any latent features outside the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 127, + 273, + 139 + ], + "spans": [ + { + "bbox": [ + 106, + 127, + 273, + 139 + ], + "score": 1.0, + "content": "set of conditionally independent features.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 106, + 143, + 505, + 264 + ], + "lines": [ + { + "bbox": [ + 105, + 142, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 142, + 505, + 156 + ], + "score": 1.0, + "content": "Causal modeling has related aims to the setting of transfer learning and guarding against adversarial", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "domain shifts. Specifically, causal models have the defining advantage that the predictions will be", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 165, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 106, + 165, + 505, + 178 + ], + "score": 1.0, + "content": "valid even under arbitrarily large interventions on all predictor variables (Haavelmo, 1944; Aldrich,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 174, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 174, + 506, + 189 + ], + "score": 1.0, + "content": "1989; Pearl, 2009; Scholkopf et al., 2012; Peters et al., 2016; Zhang et al., 2013; 2015; X. Yu, 2017; ¨", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 506, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 506, + 199 + ], + "score": 1.0, + "content": "M. Rojas-Carulla, 2017; Magliacane et al., 2017). There are two difficulties in transferring these", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 210 + ], + "score": 1.0, + "content": "results to the setting of adversarial domain changes in image classification. The first hurdle is that", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "score": 1.0, + "content": "the classification task is typically anti-causal since the image we use as a predictor is a descendant", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 219, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 505, + 232 + ], + "score": 1.0, + "content": "of the true class of the object we are interested in rather than the other way around. The second", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 505, + 243 + ], + "score": 1.0, + "content": "challenge is that we do not want to guard against arbitrary interventions on any or all variables but", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 242, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 242, + 505, + 255 + ], + "score": 1.0, + "content": "only would like to guard against a shift of the style features. It is hence not immediately obvious", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 253, + 425, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 425, + 265 + ], + "score": 1.0, + "content": "how standard causal inference can be used to guard against large domain shifts.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 106, + 270, + 505, + 511 + ], + "lines": [ + { + "bbox": [ + 105, + 268, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 505, + 284 + ], + "score": 1.0, + "content": "Recently, various approaches have been proposed that leverage causal motivations for deep learning", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 280, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 505, + 294 + ], + "score": 1.0, + "content": "or use deep learning for causal inference. In all of the following methods, the goals and the settings", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 292, + 504, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 504, + 304 + ], + "score": 1.0, + "content": "are different from ours. Specifically, the setting of anti-causal prediction and non-ancestral interven-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "tions on style variables is not considered. Various approaches focus on cause-effect inference where", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 314, + 504, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 314, + 389, + 325 + ], + "score": 1.0, + "content": "the goal is to find the causal relation between two random variables,", + "type": "text" + }, + { + "bbox": [ + 389, + 314, + 400, + 324 + ], + "score": 0.8, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 400, + 314, + 419, + 325 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 420, + 314, + 429, + 324 + ], + "score": 0.73, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 429, + 314, + 504, + 325 + ], + "score": 1.0, + "content": "(Lopez-Paz et al.,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 325, + 506, + 337 + ], + "spans": [ + { + "bbox": [ + 106, + 325, + 506, + 337 + ], + "score": 1.0, + "content": "2017; Lopez-Paz & Oquab, 2017; Goudet et al., 2017). Lopez-Paz et al. (2017) propose the Neural", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 335, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 344, + 348 + ], + "score": 1.0, + "content": "Causation Coefficient (NCC) to estimate the probability of", + "type": "text" + }, + { + "bbox": [ + 344, + 336, + 354, + 345 + ], + "score": 0.82, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 335, + 388, + 348 + ], + "score": 1.0, + "content": "causing", + "type": "text" + }, + { + "bbox": [ + 388, + 336, + 398, + 345 + ], + "score": 0.72, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 335, + 505, + 348 + ], + "score": 1.0, + "content": "and apply it to finding the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 347, + 504, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 504, + 358 + ], + "score": 1.0, + "content": "causal relations between image features. Specifically, the NCC is used to distinguish between fea-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "tures of objects and features of the objects’ contexts. Lopez-Paz & Oquab (2017) note the similarity", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 368, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 380 + ], + "score": 1.0, + "content": "between structural equation modeling and CGANs (Mirza & Osindero, 2014). One CGAN is fitted", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 169, + 392 + ], + "score": 1.0, + "content": "in the direction", + "type": "text" + }, + { + "bbox": [ + 170, + 380, + 204, + 390 + ], + "score": 0.91, + "content": "X Y", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 379, + 318, + 392 + ], + "score": 1.0, + "content": "and another one is fitted for", + "type": "text" + }, + { + "bbox": [ + 318, + 380, + 353, + 390 + ], + "score": 0.9, + "content": "Y X", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 379, + 505, + 392 + ], + "score": 1.0, + "content": ". Based on a two-sample test statistic,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "the estimated causal direction is returned. Goudet et al. (2017) use generative neural networks for", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 402, + 504, + 413 + ], + "spans": [ + { + "bbox": [ + 106, + 402, + 247, + 413 + ], + "score": 1.0, + "content": "cause-effect inference, to identify", + "type": "text" + }, + { + "bbox": [ + 247, + 403, + 253, + 411 + ], + "score": 0.74, + "content": "v", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 402, + 504, + 413 + ], + "score": 1.0, + "content": "-structures and to orient the edges of a given graph skeleton.", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 348, + 425 + ], + "score": 1.0, + "content": "Bahadori et al. (2017) devise a regularizer that combines an", + "type": "text" + }, + { + "bbox": [ + 348, + 413, + 358, + 423 + ], + "score": 0.86, + "content": "\\ell _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 358, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "penalty with weights corresponding", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "to the estimated probability of the respective feature being causal for the target. The latter estimates", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "score": 1.0, + "content": "are obtained by causality detection networks or scores such as estimated by the NCC. Besserve", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 444, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 505, + 458 + ], + "score": 1.0, + "content": "et al. (2017) draw connections between GANs and causal generative models, using a group theoretic", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 456, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 469 + ], + "score": 1.0, + "content": "framework. Kocaoglu et al. (2017) propose causal implicit generative models to sample from con-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "ditional as well as interventional distributions, using a conditional GAN architecture (CausalGAN).", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 479, + 505, + 490 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 505, + 490 + ], + "score": 1.0, + "content": "The generator structure needs to inherit its neural connections from the causal graph, i.e. the causal", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "score": 1.0, + "content": "graph structure must be known. Louizos et al. (2017) propose the use of deep latent variable models", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 500, + 347, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 347, + 512 + ], + "score": 1.0, + "content": "and proxy variables to estimate individual treatment effects.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 26.5 + }, + { + "type": "text", + "bbox": [ + 107, + 517, + 505, + 572 + ], + "lines": [ + { + "bbox": [ + 106, + 517, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 517, + 505, + 529 + ], + "score": 1.0, + "content": "Kilbertus et al. (2017) exploit causal reasoning to characterize fairness considerations in machine", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 528, + 504, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 504, + 540 + ], + "score": 1.0, + "content": "learning. Distinguishing between the protected attribute and its proxies, they derive causal non-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "score": 1.0, + "content": "discrimination criteria. The resulting algorithms avoiding proxy discrimination require classifiers to", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "be constant as a function of the proxy variables in the causal graph, thereby bearing some structural", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 561, + 231, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 231, + 573 + ], + "score": 1.0, + "content": "similarity to our style features.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 106, + 577, + 505, + 677 + ], + "lines": [ + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "score": 1.0, + "content": "Distinguishing between core and style features can be seen as some form of disentangling factors of", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 589, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 505, + 601 + ], + "score": 1.0, + "content": "variation. 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Here, we do not predefine which", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 165, + 667 + ], + "score": 1.0, + "content": "features are in", + "type": "text" + }, + { + "bbox": [ + 165, + 654, + 182, + 665 + ], + "score": 0.89, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 182, + 654, + 505, + 667 + ], + "score": 1.0, + "content": ". It could be location but also image quality, posture, brightness, background and", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 666, + 504, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 504, + 678 + ], + "score": 1.0, + "content": "contextual information. Additionally, the approach in Matsuo et al. 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There are two difficulties in transferring these", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 198, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 506, + 210 + ], + "score": 1.0, + "content": "results to the setting of adversarial domain changes in image classification. The first hurdle is that", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "score": 1.0, + "content": "the classification task is typically anti-causal since the image we use as a predictor is a descendant", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 219, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 219, + 505, + 232 + ], + "score": 1.0, + "content": "of the true class of the object we are interested in rather than the other way around. The second", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 230, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 505, + 243 + ], + "score": 1.0, + "content": "challenge is that we do not want to guard against arbitrary interventions on any or all variables but", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 242, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 242, + 505, + 255 + ], + "score": 1.0, + "content": "only would like to guard against a shift of the style features. It is hence not immediately obvious", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 253, + 425, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 425, + 265 + ], + "score": 1.0, + "content": "how standard causal inference can be used to guard against large domain shifts.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 142, + 506, + 265 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 270, + 505, + 511 + ], + "lines": [ + { + "bbox": [ + 105, + 268, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 268, + 505, + 284 + ], + "score": 1.0, + "content": "Recently, various approaches have been proposed that leverage causal motivations for deep learning", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 280, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 505, + 294 + ], + "score": 1.0, + "content": "or use deep learning for causal inference. In all of the following methods, the goals and the settings", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 292, + 504, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 504, + 304 + ], + "score": 1.0, + "content": "are different from ours. Specifically, the setting of anti-causal prediction and non-ancestral interven-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "tions on style variables is not considered. Various approaches focus on cause-effect inference where", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 314, + 504, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 314, + 389, + 325 + ], + "score": 1.0, + "content": "the goal is to find the causal relation between two random variables,", + "type": "text" + }, + { + "bbox": [ + 389, + 314, + 400, + 324 + ], + "score": 0.8, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 400, + 314, + 419, + 325 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 420, + 314, + 429, + 324 + ], + "score": 0.73, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 429, + 314, + 504, + 325 + ], + "score": 1.0, + "content": "(Lopez-Paz et al.,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 325, + 506, + 337 + ], + "spans": [ + { + "bbox": [ + 106, + 325, + 506, + 337 + ], + "score": 1.0, + "content": "2017; Lopez-Paz & Oquab, 2017; Goudet et al., 2017). Lopez-Paz et al. (2017) propose the Neural", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 335, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 335, + 344, + 348 + ], + "score": 1.0, + "content": "Causation Coefficient (NCC) to estimate the probability of", + "type": "text" + }, + { + "bbox": [ + 344, + 336, + 354, + 345 + ], + "score": 0.82, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 335, + 388, + 348 + ], + "score": 1.0, + "content": "causing", + "type": "text" + }, + { + "bbox": [ + 388, + 336, + 398, + 345 + ], + "score": 0.72, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 335, + 505, + 348 + ], + "score": 1.0, + "content": "and apply it to finding the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 347, + 504, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 504, + 358 + ], + "score": 1.0, + "content": "causal relations between image features. Specifically, the NCC is used to distinguish between fea-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 370 + ], + "score": 1.0, + "content": "tures of objects and features of the objects’ contexts. Lopez-Paz & Oquab (2017) note the similarity", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 368, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 380 + ], + "score": 1.0, + "content": "between structural equation modeling and CGANs (Mirza & Osindero, 2014). One CGAN is fitted", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 379, + 505, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 169, + 392 + ], + "score": 1.0, + "content": "in the direction", + "type": "text" + }, + { + "bbox": [ + 170, + 380, + 204, + 390 + ], + "score": 0.91, + "content": "X Y", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 379, + 318, + 392 + ], + "score": 1.0, + "content": "and another one is fitted for", + "type": "text" + }, + { + "bbox": [ + 318, + 380, + 353, + 390 + ], + "score": 0.9, + "content": "Y X", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 379, + 505, + 392 + ], + "score": 1.0, + "content": ". Based on a two-sample test statistic,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 390, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 505, + 403 + ], + "score": 1.0, + "content": "the estimated causal direction is returned. Goudet et al. (2017) use generative neural networks for", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 402, + 504, + 413 + ], + "spans": [ + { + "bbox": [ + 106, + 402, + 247, + 413 + ], + "score": 1.0, + "content": "cause-effect inference, to identify", + "type": "text" + }, + { + "bbox": [ + 247, + 403, + 253, + 411 + ], + "score": 0.74, + "content": "v", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 402, + 504, + 413 + ], + "score": 1.0, + "content": "-structures and to orient the edges of a given graph skeleton.", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 412, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 412, + 348, + 425 + ], + "score": 1.0, + "content": "Bahadori et al. (2017) devise a regularizer that combines an", + "type": "text" + }, + { + "bbox": [ + 348, + 413, + 358, + 423 + ], + "score": 0.86, + "content": "\\ell _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 358, + 412, + 505, + 425 + ], + "score": 1.0, + "content": "penalty with weights corresponding", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 436 + ], + "score": 1.0, + "content": "to the estimated probability of the respective feature being causal for the target. The latter estimates", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "score": 1.0, + "content": "are obtained by causality detection networks or scores such as estimated by the NCC. Besserve", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 444, + 505, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 505, + 458 + ], + "score": 1.0, + "content": "et al. (2017) draw connections between GANs and causal generative models, using a group theoretic", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 456, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 505, + 469 + ], + "score": 1.0, + "content": "framework. Kocaoglu et al. (2017) propose causal implicit generative models to sample from con-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "ditional as well as interventional distributions, using a conditional GAN architecture (CausalGAN).", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 479, + 505, + 490 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 505, + 490 + ], + "score": 1.0, + "content": "The generator structure needs to inherit its neural connections from the causal graph, i.e. the causal", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 506, + 502 + ], + "score": 1.0, + "content": "graph structure must be known. Louizos et al. (2017) propose the use of deep latent variable models", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 500, + 347, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 347, + 512 + ], + "score": 1.0, + "content": "and proxy variables to estimate individual treatment effects.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 26.5, + "bbox_fs": [ + 105, + 268, + 506, + 512 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 517, + 505, + 572 + ], + "lines": [ + { + "bbox": [ + 106, + 517, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 517, + 505, + 529 + ], + "score": 1.0, + "content": "Kilbertus et al. (2017) exploit causal reasoning to characterize fairness considerations in machine", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 528, + 504, + 540 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 504, + 540 + ], + "score": 1.0, + "content": "learning. Distinguishing between the protected attribute and its proxies, they derive causal non-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 505, + 552 + ], + "score": 1.0, + "content": "discrimination criteria. The resulting algorithms avoiding proxy discrimination require classifiers to", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 550, + 505, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 550, + 505, + 562 + ], + "score": 1.0, + "content": "be constant as a function of the proxy variables in the causal graph, thereby bearing some structural", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 561, + 231, + 573 + ], + "spans": [ + { + "bbox": [ + 106, + 561, + 231, + 573 + ], + "score": 1.0, + "content": "similarity to our style features.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 517, + 505, + 573 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 577, + 505, + 677 + ], + "lines": [ + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 578, + 505, + 590 + ], + "score": 1.0, + "content": "Distinguishing between core and style features can be seen as some form of disentangling factors of", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 589, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 505, + 601 + ], + "score": 1.0, + "content": "variation. 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For a formal justification of using a causal graph and", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 299, + 414, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 342, + 311 + ], + "score": 1.0, + "content": "potential outcome notation simultaneously see Richardson", + "type": "text" + }, + { + "bbox": [ + 342, + 299, + 351, + 309 + ], + "score": 0.51, + "content": "\\&", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 299, + 414, + 311 + ], + "score": 1.0, + "content": "Robins (2013).", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 10.5 + }, + { + "type": "title", + "bbox": [ + 108, + 324, + 495, + 334 + ], + "lines": [ + { + "bbox": [ + 105, + 323, + 496, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 496, + 335 + ], + "score": 1.0, + "content": "4.3 DOMAIN ADAPTATION, ADVERSARIAL EXAMPLES AND ADVERSARIAL DOMAIN SHIFTS", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 108, + 344, + 504, + 376 + ], + "lines": [ + { + "bbox": [ + 104, + 343, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 104, + 343, + 505, + 357 + ], + "score": 1.0, + "content": "In this work, we are interested in guarding against adversarial domain shifts. 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(2016) is equivalent to ours—that is, to protect against", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 128, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 128, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "shifts in the distribution(s) of test data which we characterize by distinguishing between core", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 127, + 126, + 203, + 139 + ], + "spans": [ + { + "bbox": [ + 127, + 126, + 203, + 139 + ], + "score": 1.0, + "content": "and style features.", + "type": "text", + "cross_page": true + } + ], + "index": 4 + } + ], + "index": 46, + "bbox_fs": [ + 128, + 660, + 506, + 695 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 128, + 82, + 505, + 138 + ], + "lines": [ + { + "bbox": [ + 127, + 81, + 506, + 95 + ], + "spans": [ + { + "bbox": [ + 127, + 81, + 506, + 95 + ], + "score": 1.0, + "content": "“adversarial” to refer to adversarial interventions on the style features, while the notion of", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 127, + 92, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 127, + 92, + 505, + 106 + ], + "score": 1.0, + "content": "“adversarial” in domain adversarial neural networks describes the training procedure. Never-", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 127, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 127, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "theless, the motivation of Ganin et al. (2016) is equivalent to ours—that is, to protect against", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 128, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 128, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "shifts in the distribution(s) of test data which we characterize by distinguishing between core", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 127, + 126, + 203, + 139 + ], + "spans": [ + { + "bbox": [ + 127, + 126, + 203, + 139 + ], + "score": 1.0, + "content": "and style features.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "title", + "bbox": [ + 107, + 151, + 333, + 163 + ], + "lines": [ + { + "bbox": [ + 106, + 150, + 334, + 164 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 334, + 164 + ], + "score": 1.0, + "content": "4.4 COUNTERFACTUAL OBSERVATIONS / GROUPING", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 106, + 171, + 505, + 260 + ], + "lines": [ + { + "bbox": [ + 106, + 170, + 506, + 185 + ], + "spans": [ + { + "bbox": [ + 106, + 170, + 506, + 185 + ], + "score": 1.0, + "content": "The classical problem of causal inference is that we can never observe a counterfactual. For instance,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 183, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 260, + 194 + ], + "score": 1.0, + "content": "we can only see the health outcome", + "type": "text" + }, + { + "bbox": [ + 260, + 183, + 269, + 192 + ], + "score": 0.8, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 183, + 368, + 194 + ], + "score": 1.0, + "content": "if we take a medicine,", + "type": "text" + }, + { + "bbox": [ + 369, + 183, + 400, + 193 + ], + "score": 0.89, + "content": "T = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 183, + 437, + 194 + ], + "score": 1.0, + "content": ", or not,", + "type": "text" + }, + { + "bbox": [ + 437, + 183, + 469, + 193 + ], + "score": 0.93, + "content": "T = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 469, + 183, + 506, + 194 + ], + "score": 1.0, + "content": ", but we", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 194, + 504, + 205 + ], + "spans": [ + { + "bbox": [ + 106, + 194, + 504, + 205 + ], + "score": 1.0, + "content": "can never see both health outcomes simultaneously. The counterfactual in this context would be", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 205, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 205, + 505, + 216 + ], + "score": 1.0, + "content": "an observation where we change the treatment but hold all observed and unobserved confounders", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 216, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 106, + 216, + 211, + 228 + ], + "score": 1.0, + "content": "constant. If the treatment", + "type": "text" + }, + { + "bbox": [ + 211, + 216, + 220, + 226 + ], + "score": 0.76, + "content": "T", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 216, + 505, + 228 + ], + "score": 1.0, + "content": "changes while all other variables are kept constant, we could just read", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 224, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 104, + 224, + 212, + 241 + ], + "score": 1.0, + "content": "off the treatment effect as", + "type": "text" + }, + { + "bbox": [ + 212, + 226, + 307, + 239 + ], + "score": 0.91, + "content": "Z ( T = \\bar { 1 } ) - Z ( T = 0 )", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 224, + 317, + 241 + ], + "score": 1.0, + "content": "if", + "type": "text" + }, + { + "bbox": [ + 317, + 227, + 326, + 236 + ], + "score": 0.8, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 224, + 506, + 241 + ], + "score": 1.0, + "content": "is the health outcome of interest. Observing", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 239, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 239, + 505, + 249 + ], + "score": 1.0, + "content": "such counterfactuals is in general impossible as we can either observe the outcome under treatment", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 249, + 247, + 260 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 247, + 260 + ], + "score": 1.0, + "content": "or under no treatment but not both.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 107, + 265, + 505, + 343 + ], + "lines": [ + { + "bbox": [ + 106, + 266, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 414, + 277 + ], + "score": 1.0, + "content": "Here, we use the term counterfactual for a situation where we keep class label", + "type": "text" + }, + { + "bbox": [ + 415, + 266, + 424, + 276 + ], + "score": 0.76, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 424, + 266, + 505, + 277 + ], + "score": 1.0, + "content": "and ID constant but", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 276, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 106, + 276, + 264, + 289 + ], + "score": 1.0, + "content": "allow the value of the style intervention", + "type": "text" + }, + { + "bbox": [ + 264, + 277, + 274, + 286 + ], + "score": 0.83, + "content": "\\Delta", + "type": "inline_equation" + }, + { + "bbox": [ + 274, + 276, + 388, + 289 + ], + "score": 1.0, + "content": "to change. 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The style intervention", + "type": "text" + }, + { + "bbox": [ + 336, + 299, + 346, + 308 + ], + "score": 0.81, + "content": "\\Delta", + "type": "inline_equation" + }, + { + "bbox": [ + 346, + 299, + 495, + 310 + ], + "score": 1.0, + "content": "takes the same role as the treatment", + "type": "text" + }, + { + "bbox": [ + 495, + 299, + 504, + 308 + ], + "score": 0.79, + "content": "T", + "type": "inline_equation" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 309, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 505, + 322 + ], + "score": 1.0, + "content": "in the previous medical example. 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We know that any ‘treatment effect’ of", + "type": "text" + }, + { + "bbox": [ + 317, + 420, + 327, + 430 + ], + "score": 0.83, + "content": "\\Delta", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 419, + 505, + 432 + ], + "score": 1.0, + "content": "occurs in the space of the style or orthogonal", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 429, + 506, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 141, + 443 + ], + "score": 1.0, + "content": "features", + "type": "text" + }, + { + "bbox": [ + 141, + 430, + 158, + 441 + ], + "score": 0.89, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 158, + 429, + 343, + 443 + ], + "score": 1.0, + "content": "and not in the ‘conditionally invariant’ space", + "type": "text" + }, + { + "bbox": [ + 343, + 430, + 360, + 441 + ], + "score": 0.89, + "content": "X ^ { c i }", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 429, + 506, + 443 + ], + "score": 1.0, + "content": "and we would thus like to penalize", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 442, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 371, + 455 + ], + "score": 1.0, + "content": "any change in the classification under different style interventions", + "type": "text" + }, + { + "bbox": [ + 372, + 442, + 381, + 452 + ], + "score": 0.82, + "content": "\\Delta", + "type": "inline_equation" + }, + { + "bbox": [ + 381, + 442, + 505, + 455 + ], + "score": 1.0, + "content": "but constant class and identity", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 107, + 451, + 142, + 466 + ], + "spans": [ + { + "bbox": [ + 107, + 453, + 137, + 465 + ], + "score": 0.9, + "content": "( Y , \\mathrm { I D } )", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 451, + 142, + 466 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27.5 + }, + { + "type": "text", + "bbox": [ + 106, + 469, + 505, + 525 + ], + "lines": [ + { + "bbox": [ + 106, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 241, + 482 + ], + "score": 1.0, + "content": "Notationally, we have for sample", + "type": "text" + }, + { + "bbox": [ + 242, + 469, + 302, + 481 + ], + "score": 0.93, + "content": "i \\in \\{ 1 , \\ldots , n \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 469, + 424, + 482 + ], + "score": 1.0, + "content": "with class label and identifier", + "type": "text" + }, + { + "bbox": [ + 425, + 469, + 501, + 482 + ], + "score": 0.92, + "content": "\\left( Y , \\mathrm { I D } \\right) = \\left( y _ { i } , \\mathrm { i d } _ { i } \\right)", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 469, + 505, + 482 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 107, + 479, + 507, + 495 + ], + "spans": [ + { + "bbox": [ + 107, + 482, + 120, + 492 + ], + "score": 0.78, + "content": "m _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 120, + 479, + 194, + 495 + ], + "score": 1.0, + "content": "different images", + "type": "text" + }, + { + "bbox": [ + 194, + 481, + 254, + 493 + ], + "score": 0.89, + "content": "x ( y _ { i } , \\mathrm { i d } _ { i } , \\Delta _ { i , j } )", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 479, + 274, + 495 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 275, + 482, + 339, + 492 + ], + "score": 0.91, + "content": "j ~ = ~ 1 , \\dots , m _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 340, + 479, + 507, + 495 + ], + "score": 1.0, + "content": "under different (unobserved) values of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 107, + 491, + 506, + 506 + ], + "spans": [ + { + "bbox": [ + 107, + 492, + 172, + 504 + ], + "score": 0.9, + "content": "\\Delta _ { i , 1 } , \\ldots , \\Delta _ { i , m _ { i } }", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 491, + 193, + 506 + ], + "score": 1.0, + "content": ". 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Denote the", + "type": "text" + }, + { + "bbox": [ + 283, + 504, + 289, + 514 + ], + "score": 0.83, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 289, + 502, + 393, + 516 + ], + "score": 1.0, + "content": "-th observation of sample", + "type": "text" + }, + { + "bbox": [ + 394, + 504, + 398, + 513 + ], + "score": 0.68, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 502, + 416, + 516 + ], + "score": 1.0, + "content": ", by", + "type": "text" + }, + { + "bbox": [ + 416, + 503, + 459, + 515 + ], + "score": 0.92, + "content": "x _ { i , j } \\in \\mathbb { R } ^ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 502, + 505, + 516 + ], + "score": 1.0, + "content": ". Typically", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 107, + 513, + 315, + 527 + ], + "spans": [ + { + "bbox": [ + 107, + 514, + 138, + 524 + ], + "score": 0.89, + "content": "m _ { i } = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 513, + 279, + 527 + ], + "score": 1.0, + "content": "for most samples and occasionally", + "type": "text" + }, + { + "bbox": [ + 279, + 514, + 311, + 525 + ], + "score": 0.91, + "content": "m _ { i } \\geq 2", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 513, + 315, + 527 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33 + }, + { + "type": "title", + "bbox": [ + 106, + 537, + 328, + 548 + ], + "lines": [ + { + "bbox": [ + 106, + 537, + 329, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 329, + 549 + ], + "score": 1.0, + "content": "4.4.1 STANDARD APPROACH: POOLED ESTIMATOR", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 106, + 556, + 505, + 589 + ], + "lines": [ + { + "bbox": [ + 105, + 554, + 506, + 570 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 506, + 570 + ], + "score": 1.0, + "content": "The standard approach is to simply pool over all available observations, ignoring any grouping", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 565, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 581 + ], + "score": 1.0, + "content": "information that might be available. 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The pooled estimator in all examples is always the ridge", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "score": 1.0, + "content": "estimator with a cross-validated choice of the penalty parameter. The adversarial loss of the pooled", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 267, + 667 + ], + "score": 1.0, + "content": "estimator will in general be infinite; see", + "type": "text" + }, + { + "bbox": [ + 267, + 655, + 286, + 667 + ], + "score": 0.85, + "content": "\\ S 4 . 6", + "type": "inline_equation" + }, + { + "bbox": [ + 286, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "for a concrete example. Using Figure 2, one can show", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 664, + 504, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 390, + 678 + ], + "score": 1.0, + "content": "that the pooled estimator will work well in terms of the adversarial loss", + "type": "text" + }, + { + "bbox": [ + 390, + 666, + 411, + 677 + ], + "score": 0.91, + "content": "L _ { a d v }", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 664, + 452, + 678 + ], + "score": 1.0, + "content": "if both (i)", + "type": "text" + }, + { + "bbox": [ + 452, + 666, + 462, + 676 + ], + "score": 0.67, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 664, + 474, + 678 + ], + "score": 1.0, + "content": "⊥⊥", + "type": "text" + }, + { + "bbox": [ + 475, + 666, + 504, + 677 + ], + "score": 0.86, + "content": "X | X ^ { c i }", + "type": "inline_equation" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 675, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 140, + 689 + ], + "score": 1.0, + "content": "and (ii)", + "type": "text" + }, + { + "bbox": [ + 140, + 676, + 201, + 689 + ], + "score": 0.9, + "content": "\\mathrm { ~ \\bar { \\it Y } ~ } \\mathcal { Y } \\mathrm { ~ \\not \\ = ~ } X ^ { c i } | X ^ { \\bot }", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 675, + 486, + 689 + ], + "score": 1.0, + "content": ". 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The second condition (ii) is fulfilled if the", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 708, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 181, + 722 + ], + "score": 1.0, + "content": "relations between", + "type": "text" + }, + { + "bbox": [ + 181, + 710, + 190, + 720 + ], + "score": 0.63, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 708, + 195, + 722 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 195, + 709, + 213, + 720 + ], + "score": 0.8, + "content": "X ^ { c i }", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 708, + 236, + 722 + ], + "score": 1.0, + "content": ", and", + "type": "text" + }, + { + "bbox": [ + 236, + 710, + 253, + 720 + ], + "score": 0.89, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 708, + 456, + 722 + ], + "score": 1.0, + "content": "are not deterministic. 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From (i) and (ii), we see that the pooled estimator will work well", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 46 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 309, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 309, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 128, + 82, + 505, + 138 + ], + "lines": [], + "index": 2, + "bbox_fs": [ + 127, + 81, + 506, + 139 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 107, + 151, + 333, + 163 + ], + "lines": [ + { + "bbox": [ + 106, + 150, + 334, + 164 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 334, + 164 + ], + "score": 1.0, + "content": "4.4 COUNTERFACTUAL OBSERVATIONS / GROUPING", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 106, + 171, + 505, + 260 + ], + "lines": [ + { + "bbox": [ + 106, + 170, + 506, + 185 + ], + "spans": [ + { + "bbox": [ + 106, + 170, + 506, + 185 + ], + "score": 1.0, + "content": "The classical problem of causal inference is that we can never observe a counterfactual. For instance,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 183, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 260, + 194 + ], + "score": 1.0, + "content": "we can only see the health outcome", + "type": "text" + }, + { + "bbox": [ + 260, + 183, + 269, + 192 + ], + "score": 0.8, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 270, + 183, + 368, + 194 + ], + "score": 1.0, + "content": "if we take a medicine,", + "type": "text" + }, + { + "bbox": [ + 369, + 183, + 400, + 193 + ], + "score": 0.89, + "content": "T = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 401, + 183, + 437, + 194 + ], + "score": 1.0, + "content": ", or not,", + "type": "text" + }, + { + "bbox": [ + 437, + 183, + 469, + 193 + ], + "score": 0.93, + "content": "T = 0", + "type": "inline_equation" + }, + { + "bbox": [ + 469, + 183, + 506, + 194 + ], + "score": 1.0, + "content": ", but we", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 194, + 504, + 205 + ], + "spans": [ + { + "bbox": [ + 106, + 194, + 504, + 205 + ], + "score": 1.0, + "content": "can never see both health outcomes simultaneously. The counterfactual in this context would be", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 205, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 205, + 505, + 216 + ], + "score": 1.0, + "content": "an observation where we change the treatment but hold all observed and unobserved confounders", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 216, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 106, + 216, + 211, + 228 + ], + "score": 1.0, + "content": "constant. If the treatment", + "type": "text" + }, + { + "bbox": [ + 211, + 216, + 220, + 226 + ], + "score": 0.76, + "content": "T", + "type": "inline_equation" + }, + { + "bbox": [ + 220, + 216, + 505, + 228 + ], + "score": 1.0, + "content": "changes while all other variables are kept constant, we could just read", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 104, + 224, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 104, + 224, + 212, + 241 + ], + "score": 1.0, + "content": "off the treatment effect as", + "type": "text" + }, + { + "bbox": [ + 212, + 226, + 307, + 239 + ], + "score": 0.91, + "content": "Z ( T = \\bar { 1 } ) - Z ( T = 0 )", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 224, + 317, + 241 + ], + "score": 1.0, + "content": "if", + "type": "text" + }, + { + "bbox": [ + 317, + 227, + 326, + 236 + ], + "score": 0.8, + "content": "Z", + "type": "inline_equation" + }, + { + "bbox": [ + 326, + 224, + 506, + 241 + ], + "score": 1.0, + "content": "is the health outcome of interest. Observing", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 239, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 239, + 505, + 249 + ], + "score": 1.0, + "content": "such counterfactuals is in general impossible as we can either observe the outcome under treatment", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 249, + 247, + 260 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 247, + 260 + ], + "score": 1.0, + "content": "or under no treatment but not both.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 9.5, + "bbox_fs": [ + 104, + 170, + 506, + 260 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 265, + 505, + 343 + ], + "lines": [ + { + "bbox": [ + 106, + 266, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 414, + 277 + ], + "score": 1.0, + "content": "Here, we use the term counterfactual for a situation where we keep class label", + "type": "text" + }, + { + "bbox": [ + 415, + 266, + 424, + 276 + ], + "score": 0.76, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 424, + 266, + 505, + 277 + ], + "score": 1.0, + "content": "and ID constant but", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 276, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 106, + 276, + 264, + 289 + ], + "score": 1.0, + "content": "allow the value of the style intervention", + "type": "text" + }, + { + "bbox": [ + 264, + 277, + 274, + 286 + ], + "score": 0.83, + "content": "\\Delta", + "type": "inline_equation" + }, + { + "bbox": [ + 274, + 276, + 388, + 289 + ], + "score": 1.0, + "content": "to change. 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Assume the structural equation for the image", + "type": "text" + }, + { + "bbox": [ + 457, + 309, + 493, + 320 + ], + "score": 0.91, + "content": "X \\in \\mathbb { R } ^ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 494, + 309, + 506, + 322 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 319, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 216, + 334 + ], + "score": 1.0, + "content": "linear in the style features", + "type": "text" + }, + { + "bbox": [ + 217, + 320, + 261, + 331 + ], + "score": 0.92, + "content": "\\mathbf { \\bar { A } } ^ { \\perp } \\in \\mathbb { R } ^ { q }", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 319, + 327, + 334 + ], + "score": 1.0, + "content": "(with generally", + "type": "text" + }, + { + "bbox": [ + 328, + 321, + 360, + 332 + ], + "score": 0.88, + "content": "p \\gg q ,", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 319, + 506, + 334 + ], + "score": 1.0, + "content": "), the interventions are additive and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 310, + 344 + ], + "score": 1.0, + "content": "we use logistic regression to predict a class label", + "type": "text" + }, + { + "bbox": [ + 311, + 332, + 367, + 343 + ], + "score": 0.92, + "content": "Y \\in \\{ - 1 , 1 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 331, + 505, + 344 + ], + "score": 1.0, + "content": ". Under suitable assumptions (cf.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 343, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 505, + 354 + ], + "score": 1.0, + "content": "Assumption 1), the pooled estimator has infinite adversarial loss while the adversarial loss of the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 353, + 387, + 366 + ], + "spans": [ + { + "bbox": [ + 106, + 353, + 349, + 366 + ], + "score": 1.0, + "content": "CORE estimator converges to the optimal adversarial loss as", + "type": "text" + }, + { + "bbox": [ + 349, + 355, + 382, + 363 + ], + "score": 0.87, + "content": "n \\to \\infty", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 353, + 387, + 366 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11 + }, + { + "type": "title", + "bbox": [ + 108, + 381, + 200, + 393 + ], + "lines": [ + { + "bbox": [ + 105, + 380, + 201, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 201, + 396 + ], + "score": 1.0, + "content": "5 EXPERIMENTS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 405, + 505, + 527 + ], + "lines": [ + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 311, + 418 + ], + "score": 1.0, + "content": "We perform an array of different experiments: in", + "type": "text" + }, + { + "bbox": [ + 311, + 406, + 329, + 417 + ], + "score": 0.85, + "content": "\\ S 5 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 406, + 349, + 418 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 349, + 406, + 367, + 417 + ], + "score": 0.63, + "content": "\\ S 5 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 368, + 406, + 505, + 418 + ], + "score": 1.0, + "content": "we study how CORE can handle", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 417, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 505, + 429 + ], + "score": 1.0, + "content": "confounded training data sets and changing style features in test distributions. For the assessment", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 303, + 440 + ], + "score": 1.0, + "content": "we explicitly control the level of confounding. In", + "type": "text" + }, + { + "bbox": [ + 303, + 428, + 321, + 439 + ], + "score": 0.43, + "content": "\\ S 5 . 3", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 428, + 505, + 440 + ], + "score": 1.0, + "content": ", we consider classifying elephants and horses", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 438, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 134, + 452 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 438, + 188, + 449 + ], + "score": 0.78, + "content": "X ^ { \\perp } \\equiv c o l o r", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 438, + 205, + 452 + ], + "score": 1.0, + "content": ". In", + "type": "text" + }, + { + "bbox": [ + 205, + 439, + 218, + 451 + ], + "score": 0.83, + "content": "\\ S \\mathbf { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 438, + 451, + 452 + ], + "score": 1.0, + "content": ", we include two additional experiments: in the first one,", + "type": "text" + }, + { + "bbox": [ + 451, + 439, + 505, + 450 + ], + "score": 0.39, + "content": "Y \\equiv g e n d e r", + "type": "inline_equation" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 447, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 104, + 447, + 124, + 464 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 125, + 449, + 157, + 460 + ], + "score": 0.79, + "content": "\\begin{array} { r l } { X ^ { \\bot } } & { { } \\equiv } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 447, + 311, + 464 + ], + "score": 1.0, + "content": "wearing glasses; in the second one,", + "type": "text" + }, + { + "bbox": [ + 311, + 450, + 335, + 460 + ], + "score": 0.78, + "content": "Y \\equiv", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 447, + 424, + 464 + ], + "score": 1.0, + "content": "wearing glasses and", + "type": "text" + }, + { + "bbox": [ + 424, + 449, + 456, + 460 + ], + "score": 0.86, + "content": "\\begin{array} { r l } { X ^ { \\bot } } & { { } \\equiv } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 447, + 506, + 464 + ], + "score": 1.0, + "content": "brightness.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 461, + 505, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 353, + 473 + ], + "score": 1.0, + "content": "Additional experimental results for the settings introduced in", + "type": "text" + }, + { + "bbox": [ + 354, + 461, + 365, + 472 + ], + "score": 0.75, + "content": "\\ S 2", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 461, + 431, + 473 + ], + "score": 1.0, + "content": "can be found in", + "type": "text" + }, + { + "bbox": [ + 432, + 461, + 452, + 473 + ], + "score": 0.86, + "content": "\\mathrm { \\displaystyle \\ S C } . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 452, + 461, + 470, + 473 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 470, + 461, + 490, + 473 + ], + "score": 0.88, + "content": "\\ S { \\bf C } . 3", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 461, + 505, + 473 + ], + "score": 1.0, + "content": ". A", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 471, + 506, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 484 + ], + "score": 1.0, + "content": "TensorFlow (Abadi et al., 2015) implementation of CORE will be made available as well as further", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 482, + 505, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 505, + 495 + ], + "score": 1.0, + "content": "code necessary to reproduce the experiments. In addition to the details provided below, information", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 493, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 298, + 506 + ], + "score": 1.0, + "content": "on the employed architectures can be found in", + "type": "text" + }, + { + "bbox": [ + 298, + 494, + 318, + 505 + ], + "score": 0.87, + "content": "\\mathrm { \\{ \\ - \\hbar \\mathcal { C . 7 } } ", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 493, + 505, + 506 + ], + "score": 1.0, + "content": ". An open question is how to set the value of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 505, + 505, + 517 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 192, + 517 + ], + "score": 1.0, + "content": "the tuning parameter", + "type": "text" + }, + { + "bbox": [ + 192, + 507, + 200, + 514 + ], + "score": 0.74, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 505, + 259, + 517 + ], + "score": 1.0, + "content": "or the penalty", + "type": "text" + }, + { + "bbox": [ + 259, + 505, + 267, + 514 + ], + "score": 0.82, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 505, + 403, + 517 + ], + "score": 1.0, + "content": "in Lagrangian form. We show in", + "type": "text" + }, + { + "bbox": [ + 403, + 505, + 423, + 516 + ], + "score": 0.87, + "content": "\\mathrm { \\ S C . 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 424, + 505, + 505, + 517 + ], + "score": 1.0, + "content": "that performance is", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 516, + 291, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 280, + 528 + ], + "score": 1.0, + "content": "typically not very sensitive to the choice of", + "type": "text" + }, + { + "bbox": [ + 281, + 516, + 287, + 525 + ], + "score": 0.76, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 516, + 291, + 528 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 21 + }, + { + "type": "title", + "bbox": [ + 107, + 541, + 333, + 551 + ], + "lines": [ + { + "bbox": [ + 106, + 541, + 334, + 553 + ], + "spans": [ + { + "bbox": [ + 106, + 541, + 334, + 553 + ], + "score": 1.0, + "content": "5.1 STICKMEN IMAGE-BASED AGE CLASSIFICATION", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 560, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 506, + 574 + ], + "score": 1.0, + "content": "In this example we consider synthetically generated stickmen images (cf. Figure 3a). The target", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 570, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 161, + 585 + ], + "score": 1.0, + "content": "of interest is", + "type": "text" + }, + { + "bbox": [ + 161, + 572, + 240, + 584 + ], + "score": 0.91, + "content": "Y \\in \\{ a d u l t , c h i \\bar { l } d \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 570, + 260, + 585 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 260, + 572, + 318, + 583 + ], + "score": 0.74, + "content": "X ^ { \\dot { c i } } \\equiv h e i g h t", + "type": "inline_equation" + }, + { + "bbox": [ + 319, + 570, + 366, + 585 + ], + "score": 1.0, + "content": ". The class", + "type": "text" + }, + { + "bbox": [ + 367, + 573, + 376, + 582 + ], + "score": 0.69, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 570, + 505, + 585 + ], + "score": 1.0, + "content": "is causal for height and height", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "cannot be easily intervened on, so we consider it to be a core feature—it is a robust predictor for", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "differentiating between children and adults. 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For instance, the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "score": 1.0, + "content": "images of children might mostly show children playing while the images of adults typically show", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 636, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 636, + 483, + 651 + ], + "score": 1.0, + "content": "them in more “static” postures. 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The first three images from the left have", + "type": "text" + }, + { + "bbox": [ + 463, + 213, + 501, + 224 + ], + "score": 0.86, + "content": "y \\equiv c h i l d", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 213, + 505, + 225 + ], + "score": 1.0, + "content": ";", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 222, + 505, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 226, + 235 + ], + "score": 1.0, + "content": "the remaining three images have", + "type": "text" + }, + { + "bbox": [ + 227, + 224, + 265, + 234 + ], + "score": 0.28, + "content": "y \\equiv a d u l t", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 222, + 505, + 235 + ], + "score": 1.0, + "content": ". Connected images are counterfactual examples. b) Misclassified", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 232, + 504, + 245 + ], + "spans": [ + { + "bbox": [ + 106, + 232, + 321, + 244 + ], + "score": 1.0, + "content": "observations from test set 2. c) Misclassification rates for", + "type": "text" + }, + { + "bbox": [ + 322, + 234, + 351, + 243 + ], + "score": 0.89, + "content": "c = 5 0", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 232, + 399, + 244 + ], + "score": 1.0, + "content": ". Results for", + "type": "text" + }, + { + "bbox": [ + 399, + 233, + 477, + 245 + ], + "score": 0.92, + "content": "c \\in \\{ \\bar { 2 0 } , 5 0 0 , 2 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 477, + 232, + 504, + 244 + ], + "score": 1.0, + "content": "can be", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 242, + 186, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 186, + 255 + ], + "score": 1.0, + "content": "found in Figure C.10.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "title", + "bbox": [ + 108, + 267, + 233, + 277 + ], + "lines": [ + { + "bbox": [ + 106, + 266, + 234, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 234, + 279 + ], + "score": 1.0, + "content": "4.6 THEORETICAL RESULTS", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 287, + 505, + 364 + ], + "lines": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 118, + 300 + ], + "score": 1.0, + "content": "In", + "type": "text" + }, + { + "bbox": [ + 118, + 288, + 131, + 299 + ], + "score": 0.68, + "content": "\\ S \\mathbf { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 286, + 505, + 300 + ], + "score": 1.0, + "content": "we analyze the adversarial loss, defined in Eq. (2), for the pooled and the CORE estimator", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 299, + 505, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 299, + 505, + 311 + ], + "score": 1.0, + "content": "in a one-layer network for binary classification (logistic regression). Here, we briefly sketch the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 309, + 506, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 251, + 322 + ], + "score": 1.0, + "content": "result while all details are given in", + "type": "text" + }, + { + "bbox": [ + 252, + 309, + 264, + 320 + ], + "score": 0.83, + "content": "\\ S \\mathbf { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 309, + 456, + 322 + ], + "score": 1.0, + "content": ". Assume the structural equation for the image", + "type": "text" + }, + { + "bbox": [ + 457, + 309, + 493, + 320 + ], + "score": 0.91, + "content": "X \\in \\mathbb { R } ^ { p }", + "type": "inline_equation" + }, + { + "bbox": [ + 494, + 309, + 506, + 322 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 319, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 216, + 334 + ], + "score": 1.0, + "content": "linear in the style features", + "type": "text" + }, + { + "bbox": [ + 217, + 320, + 261, + 331 + ], + "score": 0.92, + "content": "\\mathbf { \\bar { A } } ^ { \\perp } \\in \\mathbb { R } ^ { q }", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 319, + 327, + 334 + ], + "score": 1.0, + "content": "(with generally", + "type": "text" + }, + { + "bbox": [ + 328, + 321, + 360, + 332 + ], + "score": 0.88, + "content": "p \\gg q ,", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 319, + 506, + 334 + ], + "score": 1.0, + "content": "), the interventions are additive and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 310, + 344 + ], + "score": 1.0, + "content": "we use logistic regression to predict a class label", + "type": "text" + }, + { + "bbox": [ + 311, + 332, + 367, + 343 + ], + "score": 0.92, + "content": "Y \\in \\{ - 1 , 1 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 331, + 505, + 344 + ], + "score": 1.0, + "content": ". Under suitable assumptions (cf.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 343, + 505, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 505, + 354 + ], + "score": 1.0, + "content": "Assumption 1), the pooled estimator has infinite adversarial loss while the adversarial loss of the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 353, + 387, + 366 + ], + "spans": [ + { + "bbox": [ + 106, + 353, + 349, + 366 + ], + "score": 1.0, + "content": "CORE estimator converges to the optimal adversarial loss as", + "type": "text" + }, + { + "bbox": [ + 349, + 355, + 382, + 363 + ], + "score": 0.87, + "content": "n \\to \\infty", + "type": "inline_equation" + }, + { + "bbox": [ + 382, + 353, + 387, + 366 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 286, + 506, + 366 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 381, + 200, + 393 + ], + "lines": [ + { + "bbox": [ + 105, + 380, + 201, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 201, + 396 + ], + "score": 1.0, + "content": "5 EXPERIMENTS", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 405, + 505, + 527 + ], + "lines": [ + { + "bbox": [ + 106, + 406, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 406, + 311, + 418 + ], + "score": 1.0, + "content": "We perform an array of different experiments: in", + "type": "text" + }, + { + "bbox": [ + 311, + 406, + 329, + 417 + ], + "score": 0.85, + "content": "\\ S 5 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 406, + 349, + 418 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 349, + 406, + 367, + 417 + ], + "score": 0.63, + "content": "\\ S 5 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 368, + 406, + 505, + 418 + ], + "score": 1.0, + "content": "we study how CORE can handle", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 417, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 505, + 429 + ], + "score": 1.0, + "content": "confounded training data sets and changing style features in test distributions. For the assessment", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 303, + 440 + ], + "score": 1.0, + "content": "we explicitly control the level of confounding. In", + "type": "text" + }, + { + "bbox": [ + 303, + 428, + 321, + 439 + ], + "score": 0.43, + "content": "\\ S 5 . 3", + "type": "inline_equation" + }, + { + "bbox": [ + 322, + 428, + 505, + 440 + ], + "score": 1.0, + "content": ", we consider classifying elephants and horses", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 438, + 505, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 134, + 452 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 438, + 188, + 449 + ], + "score": 0.78, + "content": "X ^ { \\perp } \\equiv c o l o r", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 438, + 205, + 452 + ], + "score": 1.0, + "content": ". In", + "type": "text" + }, + { + "bbox": [ + 205, + 439, + 218, + 451 + ], + "score": 0.83, + "content": "\\ S \\mathbf { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 438, + 451, + 452 + ], + "score": 1.0, + "content": ", we include two additional experiments: in the first one,", + "type": "text" + }, + { + "bbox": [ + 451, + 439, + 505, + 450 + ], + "score": 0.39, + "content": "Y \\equiv g e n d e r", + "type": "inline_equation" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 447, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 104, + 447, + 124, + 464 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 125, + 449, + 157, + 460 + ], + "score": 0.79, + "content": "\\begin{array} { r l } { X ^ { \\bot } } & { { } \\equiv } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 157, + 447, + 311, + 464 + ], + "score": 1.0, + "content": "wearing glasses; in the second one,", + "type": "text" + }, + { + "bbox": [ + 311, + 450, + 335, + 460 + ], + "score": 0.78, + "content": "Y \\equiv", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 447, + 424, + 464 + ], + "score": 1.0, + "content": "wearing glasses and", + "type": "text" + }, + { + "bbox": [ + 424, + 449, + 456, + 460 + ], + "score": 0.86, + "content": "\\begin{array} { r l } { X ^ { \\bot } } & { { } \\equiv } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 447, + 506, + 464 + ], + "score": 1.0, + "content": "brightness.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 461, + 505, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 353, + 473 + ], + "score": 1.0, + "content": "Additional experimental results for the settings introduced in", + "type": "text" + }, + { + "bbox": [ + 354, + 461, + 365, + 472 + ], + "score": 0.75, + "content": "\\ S 2", + "type": "inline_equation" + }, + { + "bbox": [ + 365, + 461, + 431, + 473 + ], + "score": 1.0, + "content": "can be found in", + "type": "text" + }, + { + "bbox": [ + 432, + 461, + 452, + 473 + ], + "score": 0.86, + "content": "\\mathrm { \\displaystyle \\ S C } . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 452, + 461, + 470, + 473 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 470, + 461, + 490, + 473 + ], + "score": 0.88, + "content": "\\ S { \\bf C } . 3", + "type": "inline_equation" + }, + { + "bbox": [ + 490, + 461, + 505, + 473 + ], + "score": 1.0, + "content": ". A", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 471, + 506, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 484 + ], + "score": 1.0, + "content": "TensorFlow (Abadi et al., 2015) implementation of CORE will be made available as well as further", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 482, + 505, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 505, + 495 + ], + "score": 1.0, + "content": "code necessary to reproduce the experiments. In addition to the details provided below, information", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 493, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 106, + 493, + 298, + 506 + ], + "score": 1.0, + "content": "on the employed architectures can be found in", + "type": "text" + }, + { + "bbox": [ + 298, + 494, + 318, + 505 + ], + "score": 0.87, + "content": "\\mathrm { \\{ \\ - \\hbar \\mathcal { C . 7 } } ", + "type": "inline_equation" + }, + { + "bbox": [ + 318, + 493, + 505, + 506 + ], + "score": 1.0, + "content": ". An open question is how to set the value of", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 505, + 505, + 517 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 192, + 517 + ], + "score": 1.0, + "content": "the tuning parameter", + "type": "text" + }, + { + "bbox": [ + 192, + 507, + 200, + 514 + ], + "score": 0.74, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 200, + 505, + 259, + 517 + ], + "score": 1.0, + "content": "or the penalty", + "type": "text" + }, + { + "bbox": [ + 259, + 505, + 267, + 514 + ], + "score": 0.82, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 505, + 403, + 517 + ], + "score": 1.0, + "content": "in Lagrangian form. We show in", + "type": "text" + }, + { + "bbox": [ + 403, + 505, + 423, + 516 + ], + "score": 0.87, + "content": "\\mathrm { \\ S C . 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 424, + 505, + 505, + 517 + ], + "score": 1.0, + "content": "that performance is", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 516, + 291, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 280, + 528 + ], + "score": 1.0, + "content": "typically not very sensitive to the choice of", + "type": "text" + }, + { + "bbox": [ + 281, + 516, + 287, + 525 + ], + "score": 0.76, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 516, + 291, + 528 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 21, + "bbox_fs": [ + 104, + 406, + 506, + 528 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 541, + 333, + 551 + ], + "lines": [ + { + "bbox": [ + 106, + 541, + 334, + 553 + ], + "spans": [ + { + "bbox": [ + 106, + 541, + 334, + 553 + ], + "score": 1.0, + "content": "5.1 STICKMEN IMAGE-BASED AGE CLASSIFICATION", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 660 + ], + "lines": [ + { + "bbox": [ + 105, + 560, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 506, + 574 + ], + "score": 1.0, + "content": "In this example we consider synthetically generated stickmen images (cf. Figure 3a). The target", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 570, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 161, + 585 + ], + "score": 1.0, + "content": "of interest is", + "type": "text" + }, + { + "bbox": [ + 161, + 572, + 240, + 584 + ], + "score": 0.91, + "content": "Y \\in \\{ a d u l t , c h i \\bar { l } d \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 570, + 260, + 585 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 260, + 572, + 318, + 583 + ], + "score": 0.74, + "content": "X ^ { \\dot { c i } } \\equiv h e i g h t", + "type": "inline_equation" + }, + { + "bbox": [ + 319, + 570, + 366, + 585 + ], + "score": 1.0, + "content": ". The class", + "type": "text" + }, + { + "bbox": [ + 367, + 573, + 376, + 582 + ], + "score": 0.69, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 570, + 505, + 585 + ], + "score": 1.0, + "content": "is causal for height and height", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 583, + 505, + 595 + ], + "score": 1.0, + "content": "cannot be easily intervened on, so we consider it to be a core feature—it is a robust predictor for", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "score": 1.0, + "content": "differentiating between children and adults. Additionally, there is a dependence between age and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 603, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 106, + 604, + 138, + 615 + ], + "score": 0.83, + "content": "\\begin{array} { r l } { X ^ { \\bot } } & { { } \\equiv } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 138, + 603, + 480, + 619 + ], + "score": 1.0, + "content": "movement in the training dataset which arises through the hidden common cause", + "type": "text" + }, + { + "bbox": [ + 481, + 605, + 505, + 616 + ], + "score": 0.86, + "content": "D \\equiv", + "type": "inline_equation" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 616, + 505, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 505, + 629 + ], + "score": 1.0, + "content": "place of observation. The data generating process is illustrated in Figure C.9. For instance, the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 640 + ], + "score": 1.0, + "content": "images of children might mostly show children playing while the images of adults typically show", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 636, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 636, + 483, + 651 + ], + "score": 1.0, + "content": "them in more “static” postures. If the learned model exploits this dependence for predicting", + "type": "text" + }, + { + "bbox": [ + 483, + 638, + 492, + 648 + ], + "score": 0.75, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 493, + 636, + 506, + 651 + ], + "score": 1.0, + "content": ", it", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 649, + 328, + 661 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 328, + 661 + ], + "score": 1.0, + "content": "will fail when presented images of, say, dancing adults.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 560, + 506, + 661 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "Figure 3a shows examples from the training set where large movements are associated with children", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "and small movements are associated with adults. Test set 1 follows the same distribution. In test", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 686, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 156, + 700 + ], + "score": 1.0, + "content": "sets 2 and 3", + "type": "text" + }, + { + "bbox": [ + 156, + 687, + 173, + 698 + ], + "score": 0.82, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 173, + 686, + 337, + 700 + ], + "score": 1.0, + "content": "is intervened on such that the edge from", + "type": "text" + }, + { + "bbox": [ + 338, + 688, + 347, + 698 + ], + "score": 0.83, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 686, + 359, + 700 + ], + "score": 1.0, + "content": "to", + "type": "text" + }, + { + "bbox": [ + 359, + 687, + 376, + 698 + ], + "score": 0.9, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 686, + 505, + 700 + ], + "score": 1.0, + "content": "is removed and the dependence", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 141, + 711 + ], + "score": 1.0, + "content": "between", + "type": "text" + }, + { + "bbox": [ + 142, + 699, + 151, + 709 + ], + "score": 0.74, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 698, + 169, + 711 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 169, + 698, + 186, + 709 + ], + "score": 0.9, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 698, + 505, + 711 + ], + "score": 1.0, + "content": "vanishes. In test sets 2 and 3 large movements are associated with both children", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "and adults, while the movements are heavier in test set 3 than in test set 2. Figure C.10 shows exam-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 733 + ], + "score": 1.0, + "content": "ples from all test sets. Figure 3c shows misclassification rates for CORE and the pooled estimator", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 288, + 505, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 121, + 301 + ], + "score": 1.0, + "content": "for", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 121, + 289, + 152, + 299 + ], + "score": 0.89, + "content": "c = 5 0", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 153, + 288, + 263, + 301 + ], + "score": 1.0, + "content": "with a total sample size of", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 264, + 289, + 314, + 299 + ], + "score": 0.88, + "content": "m = 2 0 0 0 0", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 314, + 288, + 505, + 301 + ], + "score": 1.0, + "content": ". For as few as 50 counterfactual observations,", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 299, + 505, + 313 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 505, + 313 + ], + "score": 1.0, + "content": "CORE succeeds in achieving good predictive performance on test sets 2 and 3 where the pooled", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 215, + 323 + ], + "score": 1.0, + "content": "estimator fails (test errors", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 216, + 311, + 249, + 322 + ], + "score": 0.88, + "content": "> 4 0 \\%", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 249, + 311, + 505, + 323 + ], + "score": 1.0, + "content": "). These results suggest that the learned representation of the", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 322, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 506, + 334 + ], + "score": 1.0, + "content": "pooled estimator uses movement as a predictor for age while CORE does not use this feature due to", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 333, + 506, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 506, + 345 + ], + "score": 1.0, + "content": "the counterfactual regularization. Importantly, including more counterfactual examples would not", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 344, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 506, + 356 + ], + "score": 1.0, + "content": "improve the performance of the pooled estimator as these would be subject to the same bias and", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 355, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 506, + 367 + ], + "score": 1.0, + "content": "hence also predominantly have examples of heavily moving children and “static” adults (also see", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 365, + 342, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 253, + 379 + ], + "score": 1.0, + "content": "Figure C.10 which shows results for", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 253, + 365, + 336, + 378 + ], + "score": 0.91, + "content": "\\bar { c ^ { \\cdot } } \\in \\{ 2 0 , 5 0 0 , 2 0 0 0 \\} )", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 337, + 365, + 342, + 379 + ], + "score": 1.0, + "content": ".", + "type": "text", + "cross_page": true + } + ], + "index": 14 + } + ], + "index": 39.5, + "bbox_fs": [ + 105, + 665, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 115, + 79, + 504, + 220 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 115, + 79, + 504, + 220 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 115, + 79, + 504, + 220 + ], + "spans": [ + { + "bbox": [ + 115, + 79, + 504, + 220 + ], + "score": 0.939, + "type": "image", + "image_path": "c87df6c0af6f6f7d2710d03791aea64ae21fedcd4df62854e2ff4a137fdb7eb2.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 115, + 79, + 504, + 126.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 115, + 126.0, + 504, + 173.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 115, + 173.0, + 504, + 220.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 223, + 505, + 264 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 222, + 506, + 236 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 506, + 236 + ], + "score": 1.0, + "content": "Figure 4: a) Examples from the CelebA image quality dataset. The first three images from the left have", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 233, + 505, + 245 + ], + "spans": [ + { + "bbox": [ + 107, + 235, + 134, + 244 + ], + "score": 0.81, + "content": "y \\equiv n o", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 233, + 284, + 245 + ], + "score": 1.0, + "content": "glasses; the remaining three images have", + "type": "text" + }, + { + "bbox": [ + 284, + 234, + 328, + 244 + ], + "score": 0.71, + "content": "y \\equiv g l a s s e s", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 233, + 505, + 245 + ], + "score": 1.0, + "content": ". Connected images are counterfactual examples.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 243, + 505, + 254 + ], + "spans": [ + { + "bbox": [ + 106, + 243, + 375, + 254 + ], + "score": 1.0, + "content": "b) Misclassified examples from the test sets. c) Misclassification rates for", + "type": "text" + }, + { + "bbox": [ + 375, + 244, + 405, + 254 + ], + "score": 0.9, + "content": "\\mu = 3 0", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 243, + 421, + 254 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 422, + 243, + 458, + 253 + ], + "score": 0.88, + "content": "c = 5 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 243, + 505, + 254 + ], + "score": 1.0, + "content": ". Results for", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 252, + 407, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 237, + 265 + ], + "score": 1.0, + "content": "different counterfactual settings and", + "type": "text" + }, + { + "bbox": [ + 238, + 253, + 301, + 264 + ], + "score": 0.93, + "content": "\\mu \\in \\{ 3 0 , 4 0 , 5 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 252, + 407, + 265 + ], + "score": 1.0, + "content": "can be found in Figure C.12.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 288, + 505, + 377 + ], + "lines": [ + { + "bbox": [ + 105, + 288, + 505, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 121, + 301 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 121, + 289, + 152, + 299 + ], + "score": 0.89, + "content": "c = 5 0", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 288, + 263, + 301 + ], + "score": 1.0, + "content": "with a total sample size of", + "type": "text" + }, + { + "bbox": [ + 264, + 289, + 314, + 299 + ], + "score": 0.88, + "content": "m = 2 0 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 314, + 288, + 505, + 301 + ], + "score": 1.0, + "content": ". For as few as 50 counterfactual observations,", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 299, + 505, + 313 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 505, + 313 + ], + "score": 1.0, + "content": "CORE succeeds in achieving good predictive performance on test sets 2 and 3 where the pooled", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 311, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 215, + 323 + ], + "score": 1.0, + "content": "estimator fails (test errors", + "type": "text" + }, + { + "bbox": [ + 216, + 311, + 249, + 322 + ], + "score": 0.88, + "content": "> 4 0 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 311, + 505, + 323 + ], + "score": 1.0, + "content": "). These results suggest that the learned representation of the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 322, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 506, + 334 + ], + "score": 1.0, + "content": "pooled estimator uses movement as a predictor for age while CORE does not use this feature due to", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 333, + 506, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 506, + 345 + ], + "score": 1.0, + "content": "the counterfactual regularization. Importantly, including more counterfactual examples would not", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 344, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 506, + 356 + ], + "score": 1.0, + "content": "improve the performance of the pooled estimator as these would be subject to the same bias and", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 355, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 506, + 367 + ], + "score": 1.0, + "content": "hence also predominantly have examples of heavily moving children and “static” adults (also see", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 365, + 342, + 379 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 253, + 379 + ], + "score": 1.0, + "content": "Figure C.10 which shows results for", + "type": "text" + }, + { + "bbox": [ + 253, + 365, + 336, + 378 + ], + "score": 0.91, + "content": "\\bar { c ^ { \\cdot } } \\in \\{ 2 0 , 5 0 0 , 2 0 0 0 \\} )", + "type": "inline_equation" + }, + { + "bbox": [ + 337, + 365, + 342, + 379 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 10.5 + }, + { + "type": "title", + "bbox": [ + 107, + 405, + 382, + 415 + ], + "lines": [ + { + "bbox": [ + 105, + 404, + 384, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 404, + 384, + 417 + ], + "score": 1.0, + "content": "5.2 EYEGLASSES DETECTION: IMAGE QUALITY INTERVENTION", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 430, + 505, + 551 + ], + "lines": [ + { + "bbox": [ + 106, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 430, + 129, + 443 + ], + "score": 1.0, + "content": "As in", + "type": "text" + }, + { + "bbox": [ + 130, + 430, + 148, + 442 + ], + "score": 0.6, + "content": "\\ S 2 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 148, + 430, + 505, + 443 + ], + "score": 1.0, + "content": ", we use the CelebA dataset and consider the problem of classifying whether the person in", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 440, + 506, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 264, + 454 + ], + "score": 1.0, + "content": "the image is wearing eyeglasses. Here,", + "type": "text" + }, + { + "bbox": [ + 264, + 441, + 281, + 451 + ], + "score": 0.9, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 440, + 506, + 454 + ], + "score": 1.0, + "content": "is the quality of the image which differs conditional on", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 450, + 506, + 467 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 119, + 462 + ], + "score": 0.84, + "content": "Y ^ { 7 }", + "type": "inline_equation" + }, + { + "bbox": [ + 119, + 450, + 506, + 467 + ], + "score": 1.0, + "content": "—if the image shows a person wearing glasses, the image quality tends to be lower. This setting", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 462, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 382, + 477 + ], + "score": 1.0, + "content": "mimics the confounding that occurred in the Russian tank legend (cf.", + "type": "text" + }, + { + "bbox": [ + 383, + 464, + 393, + 475 + ], + "score": 0.5, + "content": "\\ S 1", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 462, + 505, + 477 + ], + "score": 1.0, + "content": "). The strength of the image", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 473, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 487 + ], + "score": 1.0, + "content": "quality intervention is governed by sampling the new image quality as a percentage of the original", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 485, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 106, + 486, + 285, + 498 + ], + "score": 1.0, + "content": "image’s quality from a Gaussian distribution", + "type": "text" + }, + { + "bbox": [ + 285, + 485, + 366, + 497 + ], + "score": 0.91, + "content": "\\mathcal { N } ( \\mu = 3 0 , \\sigma = \\bar { 1 } 0 )", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 486, + 505, + 498 + ], + "score": 1.0, + "content": ". Images of people without glasses", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 496, + 504, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 381, + 509 + ], + "score": 1.0, + "content": "are not changed. Thus, we only have counterfactual observations for", + "type": "text" + }, + { + "bbox": [ + 382, + 496, + 433, + 507 + ], + "score": 0.79, + "content": "Y \\equiv g l a s s e s", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 496, + 504, + 509 + ], + "score": 1.0, + "content": ". Figure 4a shows", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 507, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 506, + 519 + ], + "score": 1.0, + "content": "examples from the training set. Here, we use as the counterfactual observation the same image but", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 517, + 506, + 532 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 307, + 532 + ], + "score": 1.0, + "content": "with a newly sampled image quality value from", + "type": "text" + }, + { + "bbox": [ + 308, + 518, + 350, + 530 + ], + "score": 0.92, + "content": "\\mathcal { N } ( 3 0 , 1 0 )", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 517, + 506, + 532 + ], + "score": 1.0, + "content": ". We call using the same image as a", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 528, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 214, + 541 + ], + "score": 1.0, + "content": "counterfactual “CF setting", + "type": "text" + }, + { + "bbox": [ + 214, + 529, + 225, + 539 + ], + "score": 0.56, + "content": "1 ^ { \\circ }", + "type": "inline_equation" + }, + { + "bbox": [ + 225, + 528, + 506, + 541 + ], + "score": 1.0, + "content": ". Two alternatives for constructing counterfactual observations for this", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 540, + 366, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 201, + 552 + ], + "score": 1.0, + "content": "setting are discussed in", + "type": "text" + }, + { + "bbox": [ + 201, + 540, + 228, + 551 + ], + "score": 0.8, + "content": "\\ S \\mathbf { B } . 2 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 540, + 257, + 552 + ], + "score": 1.0, + "content": ". Here,", + "type": "text" + }, + { + "bbox": [ + 257, + 540, + 296, + 550 + ], + "score": 0.89, + "content": "c = 5 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 540, + 314, + 552 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 314, + 540, + 362, + 550 + ], + "score": 0.89, + "content": "m = 2 0 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 540, + 366, + 552 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 106, + 556, + 505, + 688 + ], + "lines": [ + { + "bbox": [ + 106, + 557, + 505, + 569 + ], + "spans": [ + { + "bbox": [ + 106, + 557, + 505, + 569 + ], + "score": 1.0, + "content": "Figure 4c shows misclassification rates for CORE and the pooled estimator on different test sets.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 568, + 506, + 580 + ], + "spans": [ + { + "bbox": [ + 106, + 568, + 506, + 580 + ], + "score": 1.0, + "content": "Examples from all test sets can be found in Figure C.11. Test set 1 follows the same distribution as", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "score": 1.0, + "content": "the training set. In test set 2 the class of the quality intervention is reversed, i.e. the quality of images", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 590, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 104, + 590, + 505, + 603 + ], + "score": 1.0, + "content": "showing people without glasses tends to be lower. In test set 3 all images are left unchanged and in", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 601, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 505, + 613 + ], + "score": 1.0, + "content": "test set 4 the quality of all images is decreased. First, we notice that the pooled estimator performs", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 612, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 505, + 624 + ], + "score": 1.0, + "content": "better than CORE on test set 1. This can be explained by the fact that it can exploit the predictive", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 623, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 505, + 635 + ], + "score": 1.0, + "content": "information contained in an image’s quality while CORE is restricted not to do so. Second, we", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 632, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 647 + ], + "score": 1.0, + "content": "observe that the pooled estimator does not perform well on test sets 2–4 as its learned representation", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "score": 1.0, + "content": "seems to use the image’s quality as a predictor for the target. In contrast, the predictive performance", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 655, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 668 + ], + "score": 1.0, + "content": "of CORE is hardly affected by the changing image quality distributions. More experimental details", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 666, + 505, + 680 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 169, + 680 + ], + "score": 1.0, + "content": "are provided in", + "type": "text" + }, + { + "bbox": [ + 170, + 667, + 190, + 678 + ], + "score": 0.89, + "content": "\\ S C . 5", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 666, + 415, + 680 + ], + "score": 1.0, + "content": ". 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Connected images are counterfactual examples.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 243, + 505, + 254 + ], + "spans": [ + { + "bbox": [ + 106, + 243, + 375, + 254 + ], + "score": 1.0, + "content": "b) Misclassified examples from the test sets. c) Misclassification rates for", + "type": "text" + }, + { + "bbox": [ + 375, + 244, + 405, + 254 + ], + "score": 0.9, + "content": "\\mu = 3 0", + "type": "inline_equation" + }, + { + "bbox": [ + 405, + 243, + 421, + 254 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 422, + 243, + 458, + 253 + ], + "score": 0.88, + "content": "c = 5 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 243, + 505, + 254 + ], + "score": 1.0, + "content": ". Results for", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 252, + 407, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 252, + 237, + 265 + ], + "score": 1.0, + "content": "different counterfactual settings and", + "type": "text" + }, + { + "bbox": [ + 238, + 253, + 301, + 264 + ], + "score": 0.93, + "content": "\\mu \\in \\{ 3 0 , 4 0 , 5 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 252, + 407, + 265 + ], + "score": 1.0, + "content": "can be found in Figure C.12.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 288, + 505, + 377 + ], + "lines": [], + "index": 10.5, + "bbox_fs": [ + 105, + 288, + 506, + 379 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 107, + 405, + 382, + 415 + ], + "lines": [ + { + "bbox": [ + 105, + 404, + 384, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 404, + 384, + 417 + ], + "score": 1.0, + "content": "5.2 EYEGLASSES DETECTION: IMAGE QUALITY INTERVENTION", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 430, + 505, + 551 + ], + "lines": [ + { + "bbox": [ + 106, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 430, + 129, + 443 + ], + "score": 1.0, + "content": "As in", + "type": "text" + }, + { + "bbox": [ + 130, + 430, + 148, + 442 + ], + "score": 0.6, + "content": "\\ S 2 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 148, + 430, + 505, + 443 + ], + "score": 1.0, + "content": ", we use the CelebA dataset and consider the problem of classifying whether the person in", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 440, + 506, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 264, + 454 + ], + "score": 1.0, + "content": "the image is wearing eyeglasses. Here,", + "type": "text" + }, + { + "bbox": [ + 264, + 441, + 281, + 451 + ], + "score": 0.9, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 440, + 506, + 454 + ], + "score": 1.0, + "content": "is the quality of the image which differs conditional on", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 450, + 506, + 467 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 119, + 462 + ], + "score": 0.84, + "content": "Y ^ { 7 }", + "type": "inline_equation" + }, + { + "bbox": [ + 119, + 450, + 506, + 467 + ], + "score": 1.0, + "content": "—if the image shows a person wearing glasses, the image quality tends to be lower. This setting", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 462, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 382, + 477 + ], + "score": 1.0, + "content": "mimics the confounding that occurred in the Russian tank legend (cf.", + "type": "text" + }, + { + "bbox": [ + 383, + 464, + 393, + 475 + ], + "score": 0.5, + "content": "\\ S 1", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 462, + 505, + 477 + ], + "score": 1.0, + "content": "). The strength of the image", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 473, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 487 + ], + "score": 1.0, + "content": "quality intervention is governed by sampling the new image quality as a percentage of the original", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 485, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 106, + 486, + 285, + 498 + ], + "score": 1.0, + "content": "image’s quality from a Gaussian distribution", + "type": "text" + }, + { + "bbox": [ + 285, + 485, + 366, + 497 + ], + "score": 0.91, + "content": "\\mathcal { N } ( \\mu = 3 0 , \\sigma = \\bar { 1 } 0 )", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 486, + 505, + 498 + ], + "score": 1.0, + "content": ". Images of people without glasses", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 496, + 504, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 381, + 509 + ], + "score": 1.0, + "content": "are not changed. Thus, we only have counterfactual observations for", + "type": "text" + }, + { + "bbox": [ + 382, + 496, + 433, + 507 + ], + "score": 0.79, + "content": "Y \\equiv g l a s s e s", + "type": "inline_equation" + }, + { + "bbox": [ + 434, + 496, + 504, + 509 + ], + "score": 1.0, + "content": ". Figure 4a shows", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 507, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 506, + 519 + ], + "score": 1.0, + "content": "examples from the training set. Here, we use as the counterfactual observation the same image but", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 517, + 506, + 532 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 307, + 532 + ], + "score": 1.0, + "content": "with a newly sampled image quality value from", + "type": "text" + }, + { + "bbox": [ + 308, + 518, + 350, + 530 + ], + "score": 0.92, + "content": "\\mathcal { N } ( 3 0 , 1 0 )", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 517, + 506, + 532 + ], + "score": 1.0, + "content": ". 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Test set 1 follows the same distribution as", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 578, + 505, + 591 + ], + "score": 1.0, + "content": "the training set. In test set 2 the class of the quality intervention is reversed, i.e. the quality of images", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 590, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 104, + 590, + 505, + 603 + ], + "score": 1.0, + "content": "showing people without glasses tends to be lower. In test set 3 all images are left unchanged and in", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 601, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 505, + 613 + ], + "score": 1.0, + "content": "test set 4 the quality of all images is decreased. 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Second, we", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 632, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 647 + ], + "score": 1.0, + "content": "observe that the pooled estimator does not perform well on test sets 2–4 as its learned representation", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 644, + 505, + 657 + ], + "score": 1.0, + "content": "seems to use the image’s quality as a predictor for the target. In contrast, the predictive performance", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 655, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 668 + ], + "score": 1.0, + "content": "of CORE is hardly affected by the changing image quality distributions. 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The first three images from the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 233, + 505, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 505, + 245 + ], + "score": 1.0, + "content": "left shows horses, the remaining three images show elephants. Connected images are counterfactual examples.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 243, + 362, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 362, + 255 + ], + "score": 1.0, + "content": "b) Misclassified examples from the test sets. c) Misclassification rates.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 108, + 266, + 231, + 277 + ], + "lines": [ + { + "bbox": [ + 105, + 265, + 232, + 278 + ], + "spans": [ + { + "bbox": [ + 105, + 265, + 232, + 278 + ], + "score": 1.0, + "content": "5.3 ELMER THE ELEPHANT", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 286, + 504, + 342 + ], + "lines": [ + { + "bbox": [ + 105, + 285, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 384, + 299 + ], + "score": 1.0, + "content": "In this example, we want to assess whether invariance with respect to", + "type": "text" + }, + { + "bbox": [ + 385, + 285, + 436, + 297 + ], + "score": 0.74, + "content": "X ^ { \\perp } \\equiv c o l o r", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 285, + 505, + 299 + ], + "score": 1.0, + "content": "can be achieved.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 295, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 505, + 310 + ], + "score": 1.0, + "content": "In the children’s book “Elmer the elephant”8 one instance of a colored elephant suffices to recognize", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 307, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 505, + 321 + ], + "score": 1.0, + "content": "it as being an elephant, making the color “gray” no longer an integral part of the object “elephant”.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 318, + 506, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 332 + ], + "score": 1.0, + "content": "Motivated by this process of concept formation, we would like to assess whether CORE can exclude", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 330, + 474, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 474, + 342 + ], + "score": 1.0, + "content": "“color” from its learned representation by including a few counterfactuals of different color.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 347, + 505, + 402 + ], + "lines": [ + { + "bbox": [ + 106, + 347, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 288, + 358 + ], + "score": 1.0, + "content": "We work with the “Animals with attributes", + "type": "text" + }, + { + "bbox": [ + 289, + 347, + 300, + 357 + ], + "score": 0.37, + "content": "2 ^ { \\circ }", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 347, + 505, + 358 + ], + "score": 1.0, + "content": "(AwA2) dataset (Xian et al., 2017) and consider", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 357, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 371 + ], + "score": 1.0, + "content": "classifying images of horses and elephants. The data generating process is illustrated in Figure C.14.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 368, + 505, + 382 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 383, + 382 + ], + "score": 1.0, + "content": "We include counterfactual examples by adding grayscale images for", + "type": "text" + }, + { + "bbox": [ + 384, + 369, + 419, + 379 + ], + "score": 0.88, + "content": "c = 2 5 0", + "type": "inline_equation" + }, + { + "bbox": [ + 419, + 368, + 505, + 382 + ], + "score": 1.0, + "content": "images of elephants,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 379, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 505, + 393 + ], + "score": 1.0, + "content": "i.e. counterfactuals are only available for one class and the shift in color is quite subtle. The total", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 391, + 188, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 391, + 188, + 402 + ], + "score": 1.0, + "content": "sample size is 1850.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 106, + 407, + 505, + 518 + ], + "lines": [ + { + "bbox": [ + 106, + 408, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 506, + 420 + ], + "score": 1.0, + "content": "Figure 5a shows examples from the training set and Figure 5c shows misclassification rates for", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 419, + 504, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 504, + 430 + ], + "score": 1.0, + "content": "CORE and the pooled estimator on different test sets. 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If we just pool", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 546, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 505, + 558 + ], + "score": 1.0, + "content": "over these examples, there is still a strong bias that elephants are gray. 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The data generating process is illustrated in Figure C.14.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 368, + 505, + 382 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 383, + 382 + ], + "score": 1.0, + "content": "We include counterfactual examples by adding grayscale images for", + "type": "text" + }, + { + "bbox": [ + 384, + 369, + 419, + 379 + ], + "score": 0.88, + "content": "c = 2 5 0", + "type": "inline_equation" + }, + { + "bbox": [ + 419, + 368, + 505, + 382 + ], + "score": 1.0, + "content": "images of elephants,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 379, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 505, + 393 + ], + "score": 1.0, + "content": "i.e. counterfactuals are only available for one class and the shift in color is quite subtle. The total", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 391, + 188, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 391, + 188, + 402 + ], + "score": 1.0, + "content": "sample size is 1850.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 347, + 505, + 402 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 407, + 505, + 518 + ], + "lines": [ + { + "bbox": [ + 106, + 408, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 506, + 420 + ], + "score": 1.0, + "content": "Figure 5a shows examples from the training set and Figure 5c shows misclassification rates for", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 419, + 504, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 504, + 430 + ], + "score": 1.0, + "content": "CORE and the pooled estimator on different test sets. Examples from all test sets can be found in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 429, + 506, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 506, + 442 + ], + "score": 1.0, + "content": "Figure C.13. Test set 1 contains original, colored images only. In test set 2 images of horses are in", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 441, + 506, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 506, + 454 + ], + "score": 1.0, + "content": "grayscale and the colorspace of elephant images is modified, effectively changing the color gray to", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "score": 1.0, + "content": "red-brown. Test set 3 contains grayscale images only and in test set 4 the colorspace of all images", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 462, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 292, + 475 + ], + "score": 1.0, + "content": "is shifted towards red. The details are given in", + "type": "text" + }, + { + "bbox": [ + 293, + 463, + 313, + 474 + ], + "score": 0.89, + "content": "\\mathrm { \\ S C } . 6", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 462, + 506, + 475 + ], + "score": 1.0, + "content": ". We observe that the pooled estimator does not", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 473, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 486 + ], + "score": 1.0, + "content": "perform well on test sets 2 and 3 as its learned representation seems to exploit the fact that “gray”", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 484, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 505, + 498 + ], + "score": 1.0, + "content": "is predictive for the target in the training set. Using this information helps its predictive accuracy on", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "test set 1. In contrast, the predictive performance of CORE is hardly affected by the changing color", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 506, + 162, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 162, + 518 + ], + "score": 1.0, + "content": "distributions.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 408, + 506, + 518 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 523, + 505, + 579 + ], + "lines": [ + { + "bbox": [ + 105, + 523, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 505, + 536 + ], + "score": 1.0, + "content": "It is noteworthy that a colored elephant can be recognized as an elephant by adding a few examples", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 534, + 505, + 547 + ], + "spans": [ + { + "bbox": [ + 105, + 534, + 505, + 547 + ], + "score": 1.0, + "content": "of a grayscale elephant to the very lightly colored pictures of natural elephants. If we just pool", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 546, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 505, + 558 + ], + "score": 1.0, + "content": "over these examples, there is still a strong bias that elephants are gray. The CORE estimator, in", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 556, + 505, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 505, + 569 + ], + "score": 1.0, + "content": "contrast, demands invariance of the prediction for instances of the same elephant and we can learn", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 567, + 316, + 580 + ], + "spans": [ + { + "bbox": [ + 105, + 567, + 316, + 580 + ], + "score": 1.0, + "content": "color invariance with a few added grayscale images.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 523, + 505, + 580 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 584, + 505, + 628 + ], + "lines": [ + { + "bbox": [ + 105, + 583, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 597 + ], + "score": 1.0, + "content": "While a thorough analysis in terms of fairness considerations is beyond the scope of this work, we", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 594, + 506, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 506, + 608 + ], + "score": 1.0, + "content": "would like to draw the following connection. If “color” was a protected attribute or a proxy for one,", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 606, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 606, + 505, + 618 + ], + "score": 1.0, + "content": "CORE would satisfy fairness in the sense that it would not include it in its learned representation. In", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 617, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 506, + 630 + ], + "score": 1.0, + "content": "contrast, there is no way to avoid that the pooled estimator extracts and uses “color” for its decisions.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 583, + 506, + 630 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 644, + 195, + 657 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 197, + 660 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 197, + 660 + ], + "score": 1.0, + "content": "6 CONCLUSION", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 108, + 669, + 504, + 713 + ], + "lines": [ + { + "bbox": [ + 105, + 669, + 504, + 682 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 504, + 682 + ], + "score": 1.0, + "content": "Distinguishing the latent features in an image into core and style features, we have proposed coun-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 681, + 506, + 693 + ], + "spans": [ + { + "bbox": [ + 106, + 681, + 506, + 693 + ], + "score": 1.0, + "content": "terfactual regularization (CORE) to achieve robustness with respect to arbitrarily large interventions", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 692, + 505, + 703 + ], + "spans": [ + { + "bbox": [ + 106, + 692, + 505, + 703 + ], + "score": 1.0, + "content": "on the style or conditionally invariant features. The main idea of the CORE estimator is to exploit the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 702, + 506, + 714 + ], + "spans": [ + { + "bbox": [ + 105, + 702, + 506, + 714 + ], + "score": 1.0, + "content": "fact that we often have instances of the same object in the training data. By demanding invariance of", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 83, + 506, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 506, + 94 + ], + "score": 1.0, + "content": "the classifier amongst a group of instances that relate to the same object, we can achieve invariance", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 505, + 105 + ], + "score": 1.0, + "content": "of the classification performance with respect to adversarial interventions on style features such as", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 506, + 117 + ], + "score": 1.0, + "content": "image quality, fashion type, color, or body posture. 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If the style features are known explicitly, we can achieve the", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 505, + 156 + ], + "score": 1.0, + "content": "same classification performance as standard data augmentation approaches but using fewer instances", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 153, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 505, + 167 + ], + "score": 1.0, + "content": "which, on top, do not have to be carefully balanced in the training data. Perhaps more interestingly,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "score": 1.0, + "content": "if the style features are unknown, the regularization of CORE avoids usage of them automatically by", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 176, + 506, + 190 + ], + "spans": [ + { + "bbox": [ + 104, + 176, + 506, + 190 + ], + "score": 1.0, + "content": "penalizing features that vary strongly between different instances of the same object in the training", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 186, + 129, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 186, + 129, + 200 + ], + "score": 1.0, + "content": "data.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 6.5 + }, + { + "type": "text", + "bbox": [ + 107, + 204, + 504, + 270 + ], + "lines": [ + { + "bbox": [ + 106, + 204, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 505, + 216 + ], + "score": 1.0, + "content": "An interesting line of work would be to use larger models such as Inception or large ResNet archi-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "tectures (Szegedy et al., 2015; He et al., 2016). These models have been trained to be invariant to an", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 225, + 506, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 225, + 279, + 239 + ], + "score": 1.0, + "content": "array of explicitly defined style features. In", + "type": "text" + }, + { + "bbox": [ + 280, + 226, + 299, + 238 + ], + "score": 0.86, + "content": "\\mathrm { \\ S B . l }", + "type": "inline_equation" + }, + { + "bbox": [ + 300, + 225, + 506, + 239 + ], + "score": 1.0, + "content": "we include results which show that using Inception", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 235, + 506, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 235, + 506, + 250 + ], + "score": 1.0, + "content": "V3 features does not guard against interventions on more implicit style features. We would thus", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "like to assess what benefits CORE can bring for training Inception-style models end-to-end, both in", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 259, + 390, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 390, + 272 + ], + "score": 1.0, + "content": "terms of sample efficiency and in terms of generalization performance.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 107, + 276, + 504, + 320 + ], + "lines": [ + { + "bbox": [ + 105, + 275, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 506, + 288 + ], + "score": 1.0, + "content": "While we showed some examples where the necessary grouping information is available, an inter-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "score": 1.0, + "content": "esting possible future direction would be to use video data since objects display temporal constancy", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 504, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 504, + 310 + ], + "score": 1.0, + "content": "and the temporal information can hence be used for grouping and counterfactual regularization.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 309, + 423, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 423, + 322 + ], + "score": 1.0, + "content": "Potentially an analogous approach could also help to debias word embeddings.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17.5 + } + ], + "page_idx": 11, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 26, + 309, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 26, + 309, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "12", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 126 + ], + "lines": [], + "index": 1.5, + "bbox_fs": [ + 105, + 83, + 506, + 127 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 132, + 505, + 198 + ], + "lines": [ + { + "bbox": [ + 106, + 131, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 131, + 505, + 144 + ], + "score": 1.0, + "content": "There are two main applications areas. 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We would thus", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 506, + 261 + ], + "score": 1.0, + "content": "like to assess what benefits CORE can bring for training Inception-style models end-to-end, both in", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 259, + 390, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 390, + 272 + ], + "score": 1.0, + "content": "terms of sample efficiency and in terms of generalization performance.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 204, + 506, + 272 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 276, + 504, + 320 + ], + "lines": [ + { + "bbox": [ + 105, + 275, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 506, + 288 + ], + "score": 1.0, + "content": "While we showed some examples where the necessary grouping information is available, an inter-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 300 + ], + "score": 1.0, + "content": "esting possible future direction would be to use video data since objects display temporal constancy", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 504, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 504, + 310 + ], + "score": 1.0, + "content": "and the temporal information can hence be used for grouping and counterfactual regularization.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 309, + 423, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 423, + 322 + ], + "score": 1.0, + "content": "Potentially an analogous approach could also help to debias word embeddings.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17.5, + "bbox_fs": [ + 105, + 275, + 506, + 322 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 82, + 175, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 176, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 176, + 95 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 100, + 506, + 177 + ], + "lines": [ + { + "bbox": [ + 105, + 99, + 505, + 113 + ], + "spans": [ + { + "bbox": [ + 105, + 99, + 505, + 113 + ], + "score": 1.0, + "content": "M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 115, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefow-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 122, + 505, + 135 + ], + "spans": [ + { + "bbox": [ + 116, + 122, + 505, + 135 + ], + "score": 1.0, + "content": "icz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, ´", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 116, + 133, + 505, + 145 + ], + "spans": [ + { + "bbox": [ + 116, + 133, + 505, + 145 + ], + "score": 1.0, + "content": "M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Va-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 115, + 143, + 505, + 158 + ], + "spans": [ + { + "bbox": [ + 115, + 143, + 505, + 158 + ], + "score": 1.0, + "content": "sudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng. ´", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 155, + 505, + 168 + ], + "spans": [ + { + "bbox": [ + 116, + 155, + 505, + 168 + ], + "score": 1.0, + "content": "TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. URL https:", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 164, + 409, + 180 + ], + "spans": [ + { + "bbox": [ + 116, + 164, + 409, + 180 + ], + "score": 1.0, + "content": "//www.tensorflow.org/. Software available from tensorflow.org.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 106, + 185, + 371, + 198 + ], + "lines": [ + { + "bbox": [ + 105, + 185, + 372, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 372, + 199 + ], + "score": 1.0, + "content": "J. Aldrich. Autonomy. Oxford Economic Papers, 41:15–34, 1989.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 106, + 205, + 501, + 228 + ], + "lines": [ + { + "bbox": [ + 105, + 205, + 502, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 502, + 218 + ], + "score": 1.0, + "content": "M. T. Bahadori, K. Chalupka, E. Choi, R. Chen, W. F. Stewart, and J. Sun. Causal regularization.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 216, + 417, + 229 + ], + "spans": [ + { + "bbox": [ + 115, + 216, + 417, + 229 + ], + "score": 1.0, + "content": "ArXiv e-prints, 2017. URL http://arxiv.org/abs/1702.02604.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 106, + 235, + 498, + 248 + ], + "lines": [ + { + "bbox": [ + 106, + 235, + 498, + 248 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 498, + 248 + ], + "score": 1.0, + "content": "S. Barocas and A. D. Selbst. Big Data’s Disparate Impact. 104 California Law Review 671, 2016.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 106, + 255, + 503, + 289 + ], + "lines": [ + { + "bbox": [ + 105, + 254, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 268 + ], + "score": 1.0, + "content": "M. Belkin, P. Niyogi, and V. Sindhwani. Manifold regularization: A geometric framework for", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 115, + 265, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 115, + 265, + 505, + 280 + ], + "score": 1.0, + "content": "learning from labeled and unlabeled examples. Journal of machine learning research, 7(Nov):", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 116, + 277, + 191, + 288 + ], + "spans": [ + { + "bbox": [ + 116, + 277, + 191, + 288 + ], + "score": 1.0, + "content": "2399–2434, 2006.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 297, + 503, + 320 + ], + "lines": [ + { + "bbox": [ + 105, + 295, + 504, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 504, + 310 + ], + "score": 1.0, + "content": "S. Ben-David, J. Blitzer, K. Crammer, and F. Pereira. Analysis of representations for domain adap-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 116, + 308, + 407, + 321 + ], + "spans": [ + { + "bbox": [ + 116, + 308, + 407, + 321 + ], + "score": 1.0, + "content": "tation. In Advances in Neural Information Processing Systems 19. 2007.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 105, + 327, + 504, + 350 + ], + "lines": [ + { + "bbox": [ + 106, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "M. Besserve, N. Shajarisales, B. Scholkopf, and D. Janzing. Group invariance principles for causal ¨", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 338, + 496, + 352 + ], + "spans": [ + { + "bbox": [ + 115, + 338, + 496, + 352 + ], + "score": 1.0, + "content": "generative models. ArXiv e-prints, 2017. URL http://arxiv.org/abs/1705.02212.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5 + }, + { + "type": "text", + "bbox": [ + 107, + 357, + 504, + 391 + ], + "lines": [ + { + "bbox": [ + 105, + 357, + 504, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 504, + 371 + ], + "score": 1.0, + "content": "T. Bolukbasi, K.-W. Chang, J. Y. Zou, V. Saligrama, and A. T. Kalai. Man is to computer program-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 116, + 369, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 116, + 369, + 505, + 381 + ], + "score": 1.0, + "content": "mer as woman is to homemaker? debiasing word embeddings. In Advances in Neural Information", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 116, + 380, + 237, + 392 + ], + "spans": [ + { + "bbox": [ + 116, + 380, + 237, + 392 + ], + "score": 1.0, + "content": "Processing Systems 29. 2016.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 108, + 399, + 504, + 433 + ], + "lines": [ + { + "bbox": [ + 105, + 398, + 505, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 505, + 413 + ], + "score": 1.0, + "content": "D. Bouchacourt, R. Tomioka, and S. Nowozin. Multi-level variational autoencoder: Learning", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 115, + 410, + 504, + 424 + ], + "spans": [ + { + "bbox": [ + 115, + 410, + 504, + 424 + ], + "score": 1.0, + "content": "disentangled representations from grouped observations. ArXiv e-prints, 2017. URL http:", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 117, + 422, + 278, + 434 + ], + "spans": [ + { + "bbox": [ + 117, + 422, + 278, + 434 + ], + "score": 1.0, + "content": "//arxiv.org/abs/1705.08841.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 108, + 441, + 504, + 475 + ], + "lines": [ + { + "bbox": [ + 106, + 441, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 505, + 453 + ], + "score": 1.0, + "content": "X. Chen, Y. Duan, R. Houthooft, J. Schulman, I. Sutskever, and P. Abbeel. InfoGAN: Interpretable", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 116, + 452, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 116, + 452, + 505, + 464 + ], + "score": 1.0, + "content": "Representation Learning by Information Maximizing Generative Adversarial Nets. In Advances", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 116, + 464, + 326, + 475 + ], + "spans": [ + { + "bbox": [ + 116, + 464, + 326, + 475 + ], + "score": 1.0, + "content": "in Neural Information Processing Systems 29. 2016.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 108, + 482, + 504, + 516 + ], + "lines": [ + { + "bbox": [ + 105, + 482, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 506, + 495 + ], + "score": 1.0, + "content": "K. Crawford. Artificial intelligence’s white guy problem. The New York Times, June 25", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 115, + 493, + 504, + 506 + ], + "spans": [ + { + "bbox": [ + 115, + 493, + 504, + 506 + ], + "score": 1.0, + "content": "2016, 2016. URL https://www.nytimes.com/2016/06/26/opinion/sunday/", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 115, + 504, + 405, + 517 + ], + "spans": [ + { + "bbox": [ + 115, + 504, + 405, + 517 + ], + "score": 1.0, + "content": "artificial-intelligences-white-guy-problem.html.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 108, + 524, + 504, + 547 + ], + "lines": [ + { + "bbox": [ + 105, + 522, + 506, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 537 + ], + "score": 1.0, + "content": "G. Csurka. A comprehensive survey on domain adaptation for visual applications. In Domain", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 115, + 534, + 366, + 547 + ], + "spans": [ + { + "bbox": [ + 115, + 534, + 366, + 547 + ], + "score": 1.0, + "content": "Adaptation in Computer Vision Applications., pp. 1–35. 2017.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 31.5 + }, + { + "type": "text", + "bbox": [ + 107, + 554, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 105, + 553, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 333, + 567 + ], + "score": 1.0, + "content": "J. Emspak. How a machine learns prejudice.", + "type": "text" + }, + { + "bbox": [ + 347, + 554, + 505, + 566 + ], + "score": 1.0, + "content": "Scientific American, December 29", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 115, + 564, + 504, + 578 + ], + "spans": [ + { + "bbox": [ + 115, + 565, + 178, + 576 + ], + "score": 1.0, + "content": "2016, 2016.", + "type": "text" + }, + { + "bbox": [ + 212, + 564, + 504, + 578 + ], + "score": 1.0, + "content": "URL https://www.scientificamerican.com/article/", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 115, + 576, + 309, + 588 + ], + "spans": [ + { + "bbox": [ + 115, + 576, + 309, + 588 + ], + "score": 1.0, + "content": "how-a-machine-learns-prejudice/.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 108, + 596, + 504, + 630 + ], + "lines": [ + { + "bbox": [ + 106, + 596, + 506, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 506, + 608 + ], + "score": 1.0, + "content": "Y. Ganin, E. Ustinova, H. Ajakan, P. Germain, H. Larochelle, F. Laviolette, M. Marchand, and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 116, + 606, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 116, + 606, + 506, + 621 + ], + "score": 1.0, + "content": "V. Lempitsky. Domain-adversarial training of neural networks. Journal of Machine Learning", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 116, + 617, + 209, + 630 + ], + "spans": [ + { + "bbox": [ + 116, + 617, + 209, + 630 + ], + "score": 1.0, + "content": "Research, 17(1), 2016.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 104, + 637, + 503, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 638, + 504, + 649 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 504, + 649 + ], + "score": 1.0, + "content": "M. Gong, K. Zhang, T. Liu, D. Tao, C. Glymour, and B. Scholkopf. Domain adaptation with ¨", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 116, + 648, + 497, + 661 + ], + "spans": [ + { + "bbox": [ + 116, + 648, + 497, + 661 + ], + "score": 1.0, + "content": "conditional transferable components. In International Conference on Machine Learning, 2016.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 39.5 + }, + { + "type": "text", + "bbox": [ + 106, + 668, + 504, + 691 + ], + "lines": [ + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "score": 1.0, + "content": "I. Goodfellow, J. Shlens, and C. Szegedy. Explaining and harnessing adversarial examples. In", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 116, + 679, + 365, + 692 + ], + "spans": [ + { + "bbox": [ + 116, + 679, + 365, + 692 + ], + "score": 1.0, + "content": "International Conference on Learning Representations, 2015.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41.5 + }, + { + "type": "text", + "bbox": [ + 111, + 698, + 503, + 732 + ], + "lines": [ + { + "bbox": [ + 108, + 697, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 108, + 697, + 505, + 712 + ], + "score": 1.0, + "content": "O. Goudet, D. Kalainathan, P. Caillou, D. Lopez-Paz, I. Guyon, M. Sebag, A. Tritas, and P. Tubaro.", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 115, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 115, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "Learning Functional Causal Models with Generative Neural Networks. ArXiv e-prints, 2017.", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 116, + 720, + 335, + 732 + ], + "spans": [ + { + "bbox": [ + 116, + 720, + 335, + 732 + ], + "score": 1.0, + "content": "URL https://arxiv.org/abs/1709.05321.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 44 + } + ], + "page_idx": 12, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 107, + 26, + 309, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 26, + 309, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "13", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 82, + 175, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 176, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 176, + 95 + ], + "score": 1.0, + "content": "REFERENCES", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 100, + 506, + 177 + ], + "lines": [ + { + "bbox": [ + 105, + 99, + 505, + 113 + ], + "spans": [ + { + "bbox": [ + 105, + 99, + 505, + 113 + ], + "score": 1.0, + "content": "M. Abadi, A. Agarwal, P. Barham, E. Brevdo, Z. Chen, C. Citro, G. S. Corrado, A. Davis, J. Dean,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 115, + 110, + 505, + 123 + ], + "spans": [ + { + "bbox": [ + 115, + 110, + 505, + 123 + ], + "score": 1.0, + "content": "M. Devin, S. Ghemawat, I. Goodfellow, A. Harp, G. Irving, M. Isard, Y. Jia, R. Jozefow-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 116, + 122, + 505, + 135 + ], + "spans": [ + { + "bbox": [ + 116, + 122, + 505, + 135 + ], + "score": 1.0, + "content": "icz, L. Kaiser, M. Kudlur, J. Levenberg, D. Mane, R. Monga, S. Moore, D. Murray, C. Olah, ´", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 116, + 133, + 505, + 145 + ], + "spans": [ + { + "bbox": [ + 116, + 133, + 505, + 145 + ], + "score": 1.0, + "content": "M. Schuster, J. Shlens, B. Steiner, I. Sutskever, K. Talwar, P. Tucker, V. Vanhoucke, V. Va-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 115, + 143, + 505, + 158 + ], + "spans": [ + { + "bbox": [ + 115, + 143, + 505, + 158 + ], + "score": 1.0, + "content": "sudevan, F. Viegas, O. Vinyals, P. Warden, M. Wattenberg, M. Wicke, Y. Yu, and X. Zheng. ´", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 116, + 155, + 505, + 168 + ], + "spans": [ + { + "bbox": [ + 116, + 155, + 505, + 168 + ], + "score": 1.0, + "content": "TensorFlow: Large-scale machine learning on heterogeneous systems, 2015. URL https:", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 116, + 164, + 409, + 180 + ], + "spans": [ + { + "bbox": [ + 116, + 164, + 409, + 180 + ], + "score": 1.0, + "content": "//www.tensorflow.org/. Software available from tensorflow.org.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4, + "bbox_fs": [ + 105, + 99, + 505, + 180 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 185, + 371, + 198 + ], + "lines": [ + { + "bbox": [ + 105, + 185, + 372, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 372, + 199 + ], + "score": 1.0, + "content": "J. Aldrich. Autonomy. Oxford Economic Papers, 41:15–34, 1989.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 185, + 372, + 199 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 205, + 501, + 228 + ], + "lines": [ + { + "bbox": [ + 105, + 205, + 502, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 502, + 218 + ], + "score": 1.0, + "content": "M. T. Bahadori, K. Chalupka, E. Choi, R. Chen, W. F. Stewart, and J. Sun. Causal regularization.", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 216, + 417, + 229 + ], + "spans": [ + { + "bbox": [ + 115, + 216, + 417, + 229 + ], + "score": 1.0, + "content": "ArXiv e-prints, 2017. URL http://arxiv.org/abs/1702.02604.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9.5, + "bbox_fs": [ + 105, + 205, + 502, + 229 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 235, + 498, + 248 + ], + "lines": [ + { + "bbox": [ + 106, + 235, + 498, + 248 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 498, + 248 + ], + "score": 1.0, + "content": "S. Barocas and A. D. Selbst. Big Data’s Disparate Impact. 104 California Law Review 671, 2016.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11, + "bbox_fs": [ + 106, + 235, + 498, + 248 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 255, + 503, + 289 + ], + "lines": [ + { + "bbox": [ + 105, + 254, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 268 + ], + "score": 1.0, + "content": "M. Belkin, P. Niyogi, and V. Sindhwani. Manifold regularization: A geometric framework for", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 115, + 265, + 505, + 280 + ], + "spans": [ + { + "bbox": [ + 115, + 265, + 505, + 280 + ], + "score": 1.0, + "content": "learning from labeled and unlabeled examples. Journal of machine learning research, 7(Nov):", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 116, + 277, + 191, + 288 + ], + "spans": [ + { + "bbox": [ + 116, + 277, + 191, + 288 + ], + "score": 1.0, + "content": "2399–2434, 2006.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13, + "bbox_fs": [ + 105, + 254, + 505, + 288 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 297, + 503, + 320 + ], + "lines": [ + { + "bbox": [ + 105, + 295, + 504, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 504, + 310 + ], + "score": 1.0, + "content": "S. Ben-David, J. Blitzer, K. Crammer, and F. Pereira. Analysis of representations for domain adap-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 116, + 308, + 407, + 321 + ], + "spans": [ + { + "bbox": [ + 116, + 308, + 407, + 321 + ], + "score": 1.0, + "content": "tation. In Advances in Neural Information Processing Systems 19. 2007.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 295, + 504, + 321 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 327, + 504, + 350 + ], + "lines": [ + { + "bbox": [ + 106, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "M. Besserve, N. Shajarisales, B. Scholkopf, and D. Janzing. Group invariance principles for causal ¨", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 338, + 496, + 352 + ], + "spans": [ + { + "bbox": [ + 115, + 338, + 496, + 352 + ], + "score": 1.0, + "content": "generative models. ArXiv e-prints, 2017. URL http://arxiv.org/abs/1705.02212.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17.5, + "bbox_fs": [ + 106, + 327, + 505, + 352 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 357, + 504, + 391 + ], + "lines": [ + { + "bbox": [ + 105, + 357, + 504, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 504, + 371 + ], + "score": 1.0, + "content": "T. Bolukbasi, K.-W. Chang, J. Y. Zou, V. Saligrama, and A. T. Kalai. Man is to computer program-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 116, + 369, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 116, + 369, + 505, + 381 + ], + "score": 1.0, + "content": "mer as woman is to homemaker? debiasing word embeddings. In Advances in Neural Information", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 116, + 380, + 237, + 392 + ], + "spans": [ + { + "bbox": [ + 116, + 380, + 237, + 392 + ], + "score": 1.0, + "content": "Processing Systems 29. 2016.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 357, + 505, + 392 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 399, + 504, + 433 + ], + "lines": [ + { + "bbox": [ + 105, + 398, + 505, + 413 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 505, + 413 + ], + "score": 1.0, + "content": "D. Bouchacourt, R. Tomioka, and S. Nowozin. Multi-level variational autoencoder: Learning", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 115, + 410, + 504, + 424 + ], + "spans": [ + { + "bbox": [ + 115, + 410, + 504, + 424 + ], + "score": 1.0, + "content": "disentangled representations from grouped observations. ArXiv e-prints, 2017. URL http:", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 117, + 422, + 278, + 434 + ], + "spans": [ + { + "bbox": [ + 117, + 422, + 278, + 434 + ], + "score": 1.0, + "content": "//arxiv.org/abs/1705.08841.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 23, + "bbox_fs": [ + 105, + 398, + 505, + 434 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 441, + 504, + 475 + ], + "lines": [ + { + "bbox": [ + 106, + 441, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 505, + 453 + ], + "score": 1.0, + "content": "X. Chen, Y. Duan, R. Houthooft, J. Schulman, I. Sutskever, and P. Abbeel. InfoGAN: Interpretable", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 116, + 452, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 116, + 452, + 505, + 464 + ], + "score": 1.0, + "content": "Representation Learning by Information Maximizing Generative Adversarial Nets. In Advances", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 116, + 464, + 326, + 475 + ], + "spans": [ + { + "bbox": [ + 116, + 464, + 326, + 475 + ], + "score": 1.0, + "content": "in Neural Information Processing Systems 29. 2016.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26, + "bbox_fs": [ + 106, + 441, + 505, + 475 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 482, + 504, + 516 + ], + "lines": [ + { + "bbox": [ + 105, + 482, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 506, + 495 + ], + "score": 1.0, + "content": "K. Crawford. Artificial intelligence’s white guy problem. The New York Times, June 25", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 115, + 493, + 504, + 506 + ], + "spans": [ + { + "bbox": [ + 115, + 493, + 504, + 506 + ], + "score": 1.0, + "content": "2016, 2016. URL https://www.nytimes.com/2016/06/26/opinion/sunday/", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 115, + 504, + 405, + 517 + ], + "spans": [ + { + "bbox": [ + 115, + 504, + 405, + 517 + ], + "score": 1.0, + "content": "artificial-intelligences-white-guy-problem.html.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 482, + 506, + 517 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 524, + 504, + 547 + ], + "lines": [ + { + "bbox": [ + 105, + 522, + 506, + 537 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 537 + ], + "score": 1.0, + "content": "G. Csurka. A comprehensive survey on domain adaptation for visual applications. In Domain", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 115, + 534, + 366, + 547 + ], + "spans": [ + { + "bbox": [ + 115, + 534, + 366, + 547 + ], + "score": 1.0, + "content": "Adaptation in Computer Vision Applications., pp. 1–35. 2017.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 522, + 506, + 547 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 554, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 105, + 553, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 333, + 567 + ], + "score": 1.0, + "content": "J. Emspak. How a machine learns prejudice.", + "type": "text" + }, + { + "bbox": [ + 347, + 554, + 505, + 566 + ], + "score": 1.0, + "content": "Scientific American, December 29", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 115, + 564, + 504, + 578 + ], + "spans": [ + { + "bbox": [ + 115, + 565, + 178, + 576 + ], + "score": 1.0, + "content": "2016, 2016.", + "type": "text" + }, + { + "bbox": [ + 212, + 564, + 504, + 578 + ], + "score": 1.0, + "content": "URL https://www.scientificamerican.com/article/", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 115, + 576, + 309, + 588 + ], + "spans": [ + { + "bbox": [ + 115, + 576, + 309, + 588 + ], + "score": 1.0, + "content": "how-a-machine-learns-prejudice/.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 553, + 505, + 588 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 596, + 504, + 630 + ], + "lines": [ + { + "bbox": [ + 106, + 596, + 506, + 608 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 506, + 608 + ], + "score": 1.0, + "content": "Y. Ganin, E. Ustinova, H. Ajakan, P. Germain, H. Larochelle, F. Laviolette, M. Marchand, and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 116, + 606, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 116, + 606, + 506, + 621 + ], + "score": 1.0, + "content": "V. Lempitsky. Domain-adversarial training of neural networks. Journal of Machine Learning", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 116, + 617, + 209, + 630 + ], + "spans": [ + { + "bbox": [ + 116, + 617, + 209, + 630 + ], + "score": 1.0, + "content": "Research, 17(1), 2016.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37, + "bbox_fs": [ + 106, + 596, + 506, + 630 + ] + }, + { + "type": "text", + "bbox": [ + 104, + 637, + 503, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 638, + 504, + 649 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 504, + 649 + ], + "score": 1.0, + "content": "M. Gong, K. Zhang, T. Liu, D. Tao, C. Glymour, and B. Scholkopf. Domain adaptation with ¨", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 116, + 648, + 497, + 661 + ], + "spans": [ + { + "bbox": [ + 116, + 648, + 497, + 661 + ], + "score": 1.0, + "content": "conditional transferable components. In International Conference on Machine Learning, 2016.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 39.5, + "bbox_fs": [ + 106, + 638, + 504, + 661 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 668, + 504, + 691 + ], + "lines": [ + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 668, + 505, + 681 + ], + "score": 1.0, + "content": "I. Goodfellow, J. Shlens, and C. Szegedy. Explaining and harnessing adversarial examples. In", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 116, + 679, + 365, + 692 + ], + "spans": [ + { + "bbox": [ + 116, + 679, + 365, + 692 + ], + "score": 1.0, + "content": "International Conference on Learning Representations, 2015.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 668, + 505, + 692 + ] + }, + { + "type": "list", + "bbox": [ + 111, + 698, + 503, + 732 + ], + "lines": [ + { + "bbox": [ + 108, + 697, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 108, + 697, + 505, + 712 + ], + "score": 1.0, + "content": "O. Goudet, D. Kalainathan, P. Caillou, D. Lopez-Paz, I. Guyon, M. Sebag, A. Tritas, and P. Tubaro.", + "type": "text" + } + ], + "index": 43, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 115, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "Learning Functional Causal Models with Generative Neural Networks. ArXiv e-prints, 2017.", + "type": "text" + } + ], + "index": 44, + "is_list_start_line": true + }, + { + "bbox": [ + 116, + 720, + 335, + 732 + ], + "spans": [ + { + "bbox": [ + 116, + 720, + 335, + 732 + ], + "score": 1.0, + "content": "URL https://arxiv.org/abs/1709.05321.", + "type": "text" + } + ], + "index": 45, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 82, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 96 + ], + "score": 1.0, + "content": "T. Haavelmo. The probability approach in econometrics. Econometrica, 12:S1–S115 (supplement),", + "type": "text", + "cross_page": true + } + ], + "index": 0, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 93, + 144, + 108 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 144, + 108 + ], + "score": 1.0, + "content": "1944.", + "type": "text", + "cross_page": true + } + ], + "index": 1, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 113, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 113, + 506, + 127 + ], + "score": 1.0, + "content": "K. He, X. Zhang, S. Ren, and J. Sun. Delving Deep into Rectifiers: Surpassing Human-Level", + "type": "text", + "cross_page": true + } + ], + "index": 2, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 125, + 336, + 137 + ], + "spans": [ + { + "bbox": [ + 115, + 125, + 336, + 137 + ], + "score": 1.0, + "content": "Performance on ImageNet Classification. ICCV, 2015.", + "type": "text", + "cross_page": true + } + ], + "index": 3, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 144, + 498, + 158 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 498, + 158 + ], + "score": 1.0, + "content": "K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. CVPR, 2016.", + "type": "text", + "cross_page": true + } + ], + "index": 4, + "is_list_start_line": true + }, + { + "bbox": [ + 105, + 164, + 504, + 176 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 504, + 176 + ], + "score": 1.0, + "content": "I. Higgins, L. Matthey, A. Pal, C. Burges, X. Glorot, M. Botvinick, S. Mohamed, and A. Lerchner.", + "type": "text", + "cross_page": true + } + ], + "index": 5, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 174, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 115, + 174, + 505, + 189 + ], + "score": 1.0, + "content": "beta-VAE: Learning Basic Visual Concepts with a Constrained Variational Framework. Interna-", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 186, + 335, + 198 + ], + "spans": [ + { + "bbox": [ + 115, + 186, + 335, + 198 + ], + "score": 1.0, + "content": "tional Conference on Learning Representations, 2017.", + "type": "text", + "cross_page": true + } + ], + "index": 7, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 205, + 506, + 219 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 506, + 219 + ], + "score": 1.0, + "content": "N. Kilbertus, M. Rojas-Carulla, G. Parascandolo, M. Hardt, D. Janzing, and B. Scholkopf. Avoiding ¨", + "type": "text", + "cross_page": true + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 114, + 216, + 506, + 231 + ], + "spans": [ + { + "bbox": [ + 114, + 216, + 506, + 231 + ], + "score": 1.0, + "content": "discrimination through causal reasoning. Advances in Neural Information Processing Systems,", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 228, + 143, + 241 + ], + "spans": [ + { + "bbox": [ + 115, + 228, + 143, + 241 + ], + "score": 1.0, + "content": "2017.", + "type": "text", + "cross_page": true + } + ], + "index": 10, + "is_list_end_line": true + }, + { + "bbox": [ + 106, + 247, + 441, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 247, + 441, + 259 + ], + "score": 1.0, + "content": "D. P. Kingma and J. Ba. Adam: A method for stochastic optimization. ICLR, 2015.", + "type": "text", + "cross_page": true + } + ], + "index": 11, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 266, + 506, + 281 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 506, + 281 + ], + "score": 1.0, + "content": "M. Kocaoglu, C. Snyder, A. G. Dimakis, and S. Vishwanath. CausalGAN: Learning Causal Implicit", + "type": "text", + "cross_page": true + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 277, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 115, + 277, + 505, + 292 + ], + "score": 1.0, + "content": "Generative Models with Adversarial Training. ArXiv e-prints, 2017. URL https://arxiv.", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 114, + 289, + 231, + 303 + ], + "spans": [ + { + "bbox": [ + 114, + 289, + 231, + 303 + ], + "score": 1.0, + "content": "org/abs/1709.02023.", + "type": "text", + "cross_page": true + } + ], + "index": 14, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 309, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 505, + 321 + ], + "score": 1.0, + "content": "A. Krizhevsky, I. Sutskever, and G. E Hinton. Imagenet classification with deep convolutional neural", + "type": "text", + "cross_page": true + } + ], + "index": 15, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 319, + 421, + 334 + ], + "spans": [ + { + "bbox": [ + 115, + 319, + 421, + 334 + ], + "score": 1.0, + "content": "networks. In Advances in Neural Information Processing Systems 25. 2012.", + "type": "text", + "cross_page": true + } + ], + "index": 16, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 338, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 505, + 353 + ], + "score": 1.0, + "content": "Y. LeCun and C. Cortes. MNIST handwritten digit database. 2010. URL http://yann.lecun.", + "type": "text", + "cross_page": true + } + ], + "index": 17, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 351, + 212, + 363 + ], + "spans": [ + { + "bbox": [ + 115, + 351, + 212, + 363 + ], + "score": 1.0, + "content": "com/exdb/mnist/.", + "type": "text", + "cross_page": true + } + ], + "index": 18, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 371, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 506, + 383 + ], + "score": 1.0, + "content": "Z. Liu, P. Luo, X. Wang, and X. Tang. Deep learning face attributes in the wild. In Proceedings of", + "type": "text", + "cross_page": true + } + ], + "index": 19, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 381, + 360, + 393 + ], + "spans": [ + { + "bbox": [ + 115, + 381, + 360, + 393 + ], + "score": 1.0, + "content": "International Conference on Computer Vision (ICCV), 2015.", + "type": "text", + "cross_page": true + } + ], + "index": 20, + "is_list_end_line": true + }, + { + "bbox": [ + 104, + 399, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 104, + 399, + 506, + 414 + ], + "score": 1.0, + "content": "D. Lopez-Paz and M. Oquab. Revisiting Classifier Two-Sample Tests. International Conference on", + "type": "text", + "cross_page": true + } + ], + "index": 21, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 412, + 280, + 424 + ], + "spans": [ + { + "bbox": [ + 115, + 412, + 280, + 424 + ], + "score": 1.0, + "content": "Learning Representations (ICLR), 2017.", + "type": "text", + "cross_page": true + } + ], + "index": 22, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 430, + 506, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 506, + 444 + ], + "score": 1.0, + "content": "D. Lopez-Paz, R. Nishihara, S. Chintala, B. Scholkopf, and L. Bottou. Discovering causal signals ¨", + "type": "text", + "cross_page": true + } + ], + "index": 23, + "is_list_start_line": true + }, + { + "bbox": [ + 113, + 441, + 507, + 457 + ], + "spans": [ + { + "bbox": [ + 113, + 441, + 507, + 457 + ], + "score": 1.0, + "content": "in images. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2017),", + "type": "text", + "cross_page": true + } + ], + "index": 24 + }, + { + "bbox": [ + 115, + 451, + 142, + 467 + ], + "spans": [ + { + "bbox": [ + 115, + 451, + 142, + 467 + ], + "score": 1.0, + "content": "2017.", + "type": "text", + "cross_page": true + } + ], + "index": 25, + "is_list_end_line": true + }, + { + "bbox": [ + 104, + 472, + 506, + 487 + ], + "spans": [ + { + "bbox": [ + 104, + 472, + 506, + 487 + ], + "score": 1.0, + "content": "C. Louizos, U. Shalit, J. M. Mooij, D. Sontag, R. Zemel, and M. Welling. Causal effect inference", + "type": "text", + "cross_page": true + } + ], + "index": 26, + "is_list_start_line": true + }, + { + "bbox": [ + 116, + 485, + 492, + 497 + ], + "spans": [ + { + "bbox": [ + 116, + 485, + 492, + 497 + ], + "score": 1.0, + "content": "with deep latent-variable models. Advances in Neural Information Processing Systems, 2017.", + "type": "text", + "cross_page": true + } + ], + "index": 27, + "is_list_end_line": true + }, + { + "bbox": [ + 104, + 502, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 104, + 502, + 506, + 517 + ], + "score": 1.0, + "content": "R. Turner J. Peters M. Rojas-Carulla, B. Scholkopf. Causal transfer in machine learning. ¨ ArXiv", + "type": "text", + "cross_page": true + } + ], + "index": 28, + "is_list_start_line": true + }, + { + "bbox": [ + 113, + 513, + 399, + 529 + ], + "spans": [ + { + "bbox": [ + 113, + 513, + 399, + 529 + ], + "score": 1.0, + "content": "e-prints, 2017. URL https://arxiv.org/abs/1507.05333.", + "type": "text", + "cross_page": true + } + ], + "index": 29, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 534, + 506, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 534, + 506, + 548 + ], + "score": 1.0, + "content": "S. Magliacane, T. van Ommen, T. Claassen, S. Bongers, P. Versteeg, and J. M. Mooij. Causal transfer", + "type": "text", + "cross_page": true + } + ], + "index": 30, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 545, + 462, + 559 + ], + "spans": [ + { + "bbox": [ + 115, + 545, + 462, + 559 + ], + "score": 1.0, + "content": "learning. ArXiv e-prints, 2017. URL https://arxiv.org/abs/1707.06422.", + "type": "text", + "cross_page": true + } + ], + "index": 31, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "T. Matsuo, H. Fukuhara, and N. Shimada. Transform invariant auto-encoder. ArXiv e-prints, 2017.", + "type": "text", + "cross_page": true + } + ], + "index": 32, + "is_list_start_line": true + }, + { + "bbox": [ + 114, + 574, + 331, + 590 + ], + "spans": [ + { + "bbox": [ + 114, + 574, + 331, + 590 + ], + "score": 1.0, + "content": "URL http://arxiv.org/abs/1709.03754.", + "type": "text", + "cross_page": true + } + ], + "index": 33, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 595, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 506, + 609 + ], + "score": 1.0, + "content": "M. Mirza and S. Osindero. Conditional Generative Adversarial Nets. ArXiv e-prints, 2014. URL", + "type": "text", + "cross_page": true + } + ], + "index": 34, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 608, + 308, + 620 + ], + "spans": [ + { + "bbox": [ + 115, + 608, + 308, + 620 + ], + "score": 1.0, + "content": "https://arxiv.org/abs/1411.1784.", + "type": "text", + "cross_page": true + } + ], + "index": 35, + "is_list_end_line": true + }, + { + "bbox": [ + 104, + 625, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 104, + 625, + 506, + 640 + ], + "score": 1.0, + "content": "J. Pearl. Causality: Models, Reasoning, and Inference. Cambridge University Press, New York,", + "type": "text", + "cross_page": true + } + ], + "index": 36, + "is_list_start_line": true + }, + { + "bbox": [ + 116, + 638, + 217, + 650 + ], + "spans": [ + { + "bbox": [ + 116, + 638, + 217, + 650 + ], + "score": 1.0, + "content": "USA, 2nd edition, 2009.", + "type": "text", + "cross_page": true + } + ], + "index": 37, + "is_list_end_line": true + }, + { + "bbox": [ + 104, + 655, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 104, + 655, + 505, + 671 + ], + "score": 1.0, + "content": "J. Peters, P. Buhlmann, and N. Meinshausen. Causal inference using invariant prediction: identifica- ¨", + "type": "text", + "cross_page": true + } + ], + "index": 38, + "is_list_start_line": true + }, + { + "bbox": [ + 114, + 666, + 505, + 682 + ], + "spans": [ + { + "bbox": [ + 114, + 666, + 505, + 682 + ], + "score": 1.0, + "content": "tion and confidence intervals. Journal of the Royal Statistical Society, Series B (with discussion),", + "type": "text", + "cross_page": true + } + ], + "index": 39 + }, + { + "bbox": [ + 114, + 680, + 185, + 693 + ], + "spans": [ + { + "bbox": [ + 114, + 680, + 185, + 693 + ], + "score": 1.0, + "content": "to appear, 2016.", + "type": "text", + "cross_page": true + } + ], + "index": 40, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "T. Richardson and J. M. Robins. Single world intervention graphs (SWIGs): A unification of the", + "type": "text", + "cross_page": true + } + ], + "index": 41, + "is_list_start_line": true + }, + { + "bbox": [ + 116, + 711, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 116, + 711, + 505, + 723 + ], + "score": 1.0, + "content": "counterfactual and graphical approaches to causality. Center for the Statistics and the Social", + "type": "text", + "cross_page": true + } + ], + "index": 42 + }, + { + "bbox": [ + 115, + 721, + 455, + 733 + ], + "spans": [ + { + "bbox": [ + 115, + 721, + 455, + 733 + ], + "score": 1.0, + "content": "Sciences, University of Washington Series. Working Paper 128, 30 April 2013, 2013.", + "type": "text", + "cross_page": true + } + ], + "index": 43, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 82, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 96 + ], + "score": 1.0, + "content": "Ted Sandler, John Blitzer, Partha P Talukdar, and Lyle H Ungar. Regularized learning with networks", + "type": "text", + "cross_page": true + } + ], + "index": 0, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 93, + 475, + 107 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 475, + 107 + ], + "score": 1.0, + "content": "of features. In Advances in neural information processing systems, pp. 1401–1408, 2009.", + "type": "text", + "cross_page": true + } + ], + "index": 1, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 112, + 506, + 126 + ], + "spans": [ + { + "bbox": [ + 105, + 112, + 506, + 126 + ], + "score": 1.0, + "content": "B. Scholkopf, D. Janzing, J. Peters, E. Sgouritsa, K. Zhang, and J. Mooij. On causal and anticausal ¨", + "type": "text", + "cross_page": true + } + ], + "index": 2, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 123, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 115, + 123, + 505, + 138 + ], + "score": 1.0, + "content": "learning. In Proceedings of the 29th International Conference on Machine Learning (ICML), pp.", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 117, + 135, + 191, + 147 + ], + "spans": [ + { + "bbox": [ + 117, + 135, + 191, + 147 + ], + "score": 1.0, + "content": "1255–1262, 2012.", + "type": "text", + "cross_page": true + } + ], + "index": 4, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 153, + 504, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 504, + 167 + ], + "score": 1.0, + "content": "B. Scholkopf, C. Burges, and V. Vapnik. Incorporating invariances in support vector learning ma- ¨", + "type": "text", + "cross_page": true + } + ], + "index": 5, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 164, + 257, + 177 + ], + "spans": [ + { + "bbox": [ + 115, + 164, + 257, + 177 + ], + "score": 1.0, + "content": "chines. pp. 47–52. Springer, 1996.", + "type": "text", + "cross_page": true + } + ], + "index": 6, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 182, + 506, + 197 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 506, + 197 + ], + "score": 1.0, + "content": "C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus. Intriguing", + "type": "text", + "cross_page": true + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 194, + 499, + 207 + ], + "spans": [ + { + "bbox": [ + 115, + 194, + 499, + 207 + ], + "score": 1.0, + "content": "properties of neural networks. In International Conference on Learning Representations, 2014.", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 213, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 505, + 226 + ], + "score": 1.0, + "content": "C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Ra-", + "type": "text", + "cross_page": true + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 223, + 506, + 238 + ], + "spans": [ + { + "bbox": [ + 115, + 223, + 506, + 238 + ], + "score": 1.0, + "content": "binovich. Going deeper with convolutions. In Computer Vision and Pattern Recognition (CVPR),", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 115, + 235, + 142, + 247 + ], + "spans": [ + { + "bbox": [ + 115, + 235, + 142, + 247 + ], + "score": 1.0, + "content": "2015.", + "type": "text", + "cross_page": true + } + ], + "index": 11, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "M. Gong K. Zhang D. Tao X. Yu, T. Liu. Transfer learning with label noise. ArXiv e-prints, 2017.", + "type": "text", + "cross_page": true + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 116, + 265, + 336, + 278 + ], + "spans": [ + { + "bbox": [ + 116, + 265, + 336, + 278 + ], + "score": 1.0, + "content": "URL https://arxiv.org/abs/1707.09724.", + "type": "text", + "cross_page": true + } + ], + "index": 13, + "is_list_end_line": true + }, + { + "bbox": [ + 106, + 284, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 505, + 297 + ], + "score": 1.0, + "content": "Y. Xian, C. H. Lampert, B. Schiele, and Z. Akata. Zero-shot learning - A comprehensive evaluation", + "type": "text", + "cross_page": true + } + ], + "index": 14, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 295, + 504, + 308 + ], + "spans": [ + { + "bbox": [ + 115, + 295, + 504, + 308 + ], + "score": 1.0, + "content": "of the good, the bad and the ugly. ArXiv e-prints, 2017. URL http://arxiv.org/abs/", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 115, + 306, + 181, + 318 + ], + "spans": [ + { + "bbox": [ + 115, + 306, + 181, + 318 + ], + "score": 1.0, + "content": "1707.00600.", + "type": "text", + "cross_page": true + } + ], + "index": 16, + "is_list_end_line": true + }, + { + "bbox": [ + 104, + 324, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 104, + 324, + 506, + 339 + ], + "score": 1.0, + "content": "E. Yudkowsky. Artificial intelligence as a positive and negative factor in global risk. Global catas-", + "type": "text", + "cross_page": true + } + ], + "index": 17, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 336, + 206, + 349 + ], + "spans": [ + { + "bbox": [ + 115, + 336, + 206, + 349 + ], + "score": 1.0, + "content": "trophic risks, 1, 2008.", + "type": "text", + "cross_page": true + } + ], + "index": 18, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 355, + 505, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 505, + 368 + ], + "score": 1.0, + "content": "K. Zhang, B. Scholkopf, K. Muandet, and Z. Wang. Domain adaptation under target and conditional ¨", + "type": "text", + "cross_page": true + } + ], + "index": 19, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 366, + 370, + 379 + ], + "spans": [ + { + "bbox": [ + 115, + 366, + 370, + 379 + ], + "score": 1.0, + "content": "shift. In International Conference on Machine Learning, 2013.", + "type": "text", + "cross_page": true + } + ], + "index": 20, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 384, + 506, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 506, + 398 + ], + "score": 1.0, + "content": "K. Zhang, M. Gong, and B. Scholkopf. Multi-source domain adaptation: A causal view. In ¨ Pro-", + "type": "text", + "cross_page": true + } + ], + "index": 21, + "is_list_start_line": true + }, + { + "bbox": [ + 115, + 396, + 434, + 408 + ], + "spans": [ + { + "bbox": [ + 115, + 396, + 434, + 408 + ], + "score": 1.0, + "content": "ceedings of the Twenty-Ninth AAAI Conference on Artificial Intelligence, 2015.", + "type": "text", + "cross_page": true + } + ], + "index": 22, + "is_list_end_line": true + } + ], + "index": 44, + "bbox_fs": [ + 108, + 697, + 505, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 104, + 48, + 507, + 737 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 506, + 96 + ], + "score": 1.0, + "content": "T. Haavelmo. The probability approach in econometrics. Econometrica, 12:S1–S115 (supplement),", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 93, + 144, + 108 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 144, + 108 + ], + "score": 1.0, + "content": "1944.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 113, + 506, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 113, + 506, + 127 + ], + "score": 1.0, + "content": "K. He, X. Zhang, S. Ren, and J. Sun. Delving Deep into Rectifiers: Surpassing Human-Level", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 125, + 336, + 137 + ], + "spans": [ + { + "bbox": [ + 115, + 125, + 336, + 137 + ], + "score": 1.0, + "content": "Performance on ImageNet Classification. ICCV, 2015.", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 144, + 498, + 158 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 498, + 158 + ], + "score": 1.0, + "content": "K. He, X. Zhang, S. Ren, and J. Sun. Deep residual learning for image recognition. CVPR, 2016.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 164, + 504, + 176 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 504, + 176 + ], + "score": 1.0, + "content": "I. Higgins, L. Matthey, A. Pal, C. Burges, X. Glorot, M. Botvinick, S. Mohamed, and A. Lerchner.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 174, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 115, + 174, + 505, + 189 + ], + "score": 1.0, + "content": "beta-VAE: Learning Basic Visual Concepts with a Constrained Variational Framework. Interna-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 115, + 186, + 335, + 198 + ], + "spans": [ + { + "bbox": [ + 115, + 186, + 335, + 198 + ], + "score": 1.0, + "content": "tional Conference on Learning Representations, 2017.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 205, + 506, + 219 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 506, + 219 + ], + "score": 1.0, + "content": "N. Kilbertus, M. Rojas-Carulla, G. Parascandolo, M. Hardt, D. Janzing, and B. Scholkopf. Avoiding ¨", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 114, + 216, + 506, + 231 + ], + "spans": [ + { + "bbox": [ + 114, + 216, + 506, + 231 + ], + "score": 1.0, + "content": "discrimination through causal reasoning. Advances in Neural Information Processing Systems,", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 228, + 143, + 241 + ], + "spans": [ + { + "bbox": [ + 115, + 228, + 143, + 241 + ], + "score": 1.0, + "content": "2017.", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 247, + 441, + 259 + ], + "spans": [ + { + "bbox": [ + 106, + 247, + 441, + 259 + ], + "score": 1.0, + "content": "D. P. Kingma and J. Ba. Adam: A method for stochastic optimization. ICLR, 2015.", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 266, + 506, + 281 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 506, + 281 + ], + "score": 1.0, + "content": "M. Kocaoglu, C. Snyder, A. G. Dimakis, and S. Vishwanath. CausalGAN: Learning Causal Implicit", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 115, + 277, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 115, + 277, + 505, + 292 + ], + "score": 1.0, + "content": "Generative Models with Adversarial Training. ArXiv e-prints, 2017. URL https://arxiv.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 114, + 289, + 231, + 303 + ], + "spans": [ + { + "bbox": [ + 114, + 289, + 231, + 303 + ], + "score": 1.0, + "content": "org/abs/1709.02023.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 309, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 505, + 321 + ], + "score": 1.0, + "content": "A. Krizhevsky, I. Sutskever, and G. E Hinton. Imagenet classification with deep convolutional neural", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 115, + 319, + 421, + 334 + ], + "spans": [ + { + "bbox": [ + 115, + 319, + 421, + 334 + ], + "score": 1.0, + "content": "networks. In Advances in Neural Information Processing Systems 25. 2012.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 338, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 505, + 353 + ], + "score": 1.0, + "content": "Y. LeCun and C. Cortes. MNIST handwritten digit database. 2010. URL http://yann.lecun.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 351, + 212, + 363 + ], + "spans": [ + { + "bbox": [ + 115, + 351, + 212, + 363 + ], + "score": 1.0, + "content": "com/exdb/mnist/.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 371, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 506, + 383 + ], + "score": 1.0, + "content": "Z. Liu, P. Luo, X. Wang, and X. Tang. Deep learning face attributes in the wild. In Proceedings of", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 115, + 381, + 360, + 393 + ], + "spans": [ + { + "bbox": [ + 115, + 381, + 360, + 393 + ], + "score": 1.0, + "content": "International Conference on Computer Vision (ICCV), 2015.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 399, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 104, + 399, + 506, + 414 + ], + "score": 1.0, + "content": "D. Lopez-Paz and M. Oquab. Revisiting Classifier Two-Sample Tests. International Conference on", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 115, + 412, + 280, + 424 + ], + "spans": [ + { + "bbox": [ + 115, + 412, + 280, + 424 + ], + "score": 1.0, + "content": "Learning Representations (ICLR), 2017.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 430, + 506, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 506, + 444 + ], + "score": 1.0, + "content": "D. Lopez-Paz, R. Nishihara, S. Chintala, B. Scholkopf, and L. Bottou. Discovering causal signals ¨", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 113, + 441, + 507, + 457 + ], + "spans": [ + { + "bbox": [ + 113, + 441, + 507, + 457 + ], + "score": 1.0, + "content": "in images. In The IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2017),", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 115, + 451, + 142, + 467 + ], + "spans": [ + { + "bbox": [ + 115, + 451, + 142, + 467 + ], + "score": 1.0, + "content": "2017.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 472, + 506, + 487 + ], + "spans": [ + { + "bbox": [ + 104, + 472, + 506, + 487 + ], + "score": 1.0, + "content": "C. Louizos, U. Shalit, J. M. Mooij, D. Sontag, R. Zemel, and M. Welling. Causal effect inference", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 116, + 485, + 492, + 497 + ], + "spans": [ + { + "bbox": [ + 116, + 485, + 492, + 497 + ], + "score": 1.0, + "content": "with deep latent-variable models. Advances in Neural Information Processing Systems, 2017.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 502, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 104, + 502, + 506, + 517 + ], + "score": 1.0, + "content": "R. Turner J. Peters M. Rojas-Carulla, B. Scholkopf. Causal transfer in machine learning. ¨ ArXiv", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 113, + 513, + 399, + 529 + ], + "spans": [ + { + "bbox": [ + 113, + 513, + 399, + 529 + ], + "score": 1.0, + "content": "e-prints, 2017. URL https://arxiv.org/abs/1507.05333.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 534, + 506, + 548 + ], + "spans": [ + { + "bbox": [ + 105, + 534, + 506, + 548 + ], + "score": 1.0, + "content": "S. Magliacane, T. van Ommen, T. Claassen, S. Bongers, P. Versteeg, and J. M. Mooij. Causal transfer", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 115, + 545, + 462, + 559 + ], + "spans": [ + { + "bbox": [ + 115, + 545, + 462, + 559 + ], + "score": 1.0, + "content": "learning. ArXiv e-prints, 2017. URL https://arxiv.org/abs/1707.06422.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "T. Matsuo, H. Fukuhara, and N. Shimada. Transform invariant auto-encoder. ArXiv e-prints, 2017.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 114, + 574, + 331, + 590 + ], + "spans": [ + { + "bbox": [ + 114, + 574, + 331, + 590 + ], + "score": 1.0, + "content": "URL http://arxiv.org/abs/1709.03754.", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 595, + 506, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 506, + 609 + ], + "score": 1.0, + "content": "M. Mirza and S. Osindero. Conditional Generative Adversarial Nets. ArXiv e-prints, 2014. URL", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 115, + 608, + 308, + 620 + ], + "spans": [ + { + "bbox": [ + 115, + 608, + 308, + 620 + ], + "score": 1.0, + "content": "https://arxiv.org/abs/1411.1784.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 104, + 625, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 104, + 625, + 506, + 640 + ], + "score": 1.0, + "content": "J. Pearl. Causality: Models, Reasoning, and Inference. Cambridge University Press, New York,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 116, + 638, + 217, + 650 + ], + "spans": [ + { + "bbox": [ + 116, + 638, + 217, + 650 + ], + "score": 1.0, + "content": "USA, 2nd edition, 2009.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 104, + 655, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 104, + 655, + 505, + 671 + ], + "score": 1.0, + "content": "J. Peters, P. Buhlmann, and N. Meinshausen. Causal inference using invariant prediction: identifica- ¨", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 114, + 666, + 505, + 682 + ], + "spans": [ + { + "bbox": [ + 114, + 666, + 505, + 682 + ], + "score": 1.0, + "content": "tion and confidence intervals. Journal of the Royal Statistical Society, Series B (with discussion),", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 114, + 680, + 185, + 693 + ], + "spans": [ + { + "bbox": [ + 114, + 680, + 185, + 693 + ], + "score": 1.0, + "content": "to appear, 2016.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "T. Richardson and J. M. Robins. Single world intervention graphs (SWIGs): A unification of the", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 116, + 711, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 116, + 711, + 505, + 723 + ], + "score": 1.0, + "content": "counterfactual and graphical approaches to causality. Center for the Statistics and the Social", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 115, + 721, + 455, + 733 + ], + "spans": [ + { + "bbox": [ + 115, + 721, + 455, + 733 + ], + "score": 1.0, + "content": "Sciences, University of Washington Series. Working Paper 128, 30 April 2013, 2013.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 21.5 + } + ], + "page_idx": 13, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 27, + 308, + 38 + ], + "lines": [ + { + "bbox": [ + 107, + 25, + 309, + 38 + ], + "spans": [ + { + "bbox": [ + 107, + 25, + 309, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "14", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "list", + "bbox": [ + 104, + 48, + 507, + 737 + ], + "lines": [], + "index": 21.5, + "bbox_fs": [ + 104, + 82, + 507, + 733 + ], + "lines_deleted": true + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 104, + 80, + 506, + 409 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 96 + ], + "score": 1.0, + "content": "Ted Sandler, John Blitzer, Partha P Talukdar, and Lyle H Ungar. Regularized learning with networks", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 115, + 93, + 475, + 107 + ], + "spans": [ + { + "bbox": [ + 115, + 93, + 475, + 107 + ], + "score": 1.0, + "content": "of features. In Advances in neural information processing systems, pp. 1401–1408, 2009.", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 112, + 506, + 126 + ], + "spans": [ + { + "bbox": [ + 105, + 112, + 506, + 126 + ], + "score": 1.0, + "content": "B. Scholkopf, D. Janzing, J. Peters, E. Sgouritsa, K. Zhang, and J. Mooij. On causal and anticausal ¨", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 115, + 123, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 115, + 123, + 505, + 138 + ], + "score": 1.0, + "content": "learning. In Proceedings of the 29th International Conference on Machine Learning (ICML), pp.", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 117, + 135, + 191, + 147 + ], + "spans": [ + { + "bbox": [ + 117, + 135, + 191, + 147 + ], + "score": 1.0, + "content": "1255–1262, 2012.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 153, + 504, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 504, + 167 + ], + "score": 1.0, + "content": "B. Scholkopf, C. Burges, and V. Vapnik. Incorporating invariances in support vector learning ma- ¨", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 115, + 164, + 257, + 177 + ], + "spans": [ + { + "bbox": [ + 115, + 164, + 257, + 177 + ], + "score": 1.0, + "content": "chines. pp. 47–52. Springer, 1996.", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 182, + 506, + 197 + ], + "spans": [ + { + "bbox": [ + 105, + 182, + 506, + 197 + ], + "score": 1.0, + "content": "C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus. Intriguing", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 115, + 194, + 499, + 207 + ], + "spans": [ + { + "bbox": [ + 115, + 194, + 499, + 207 + ], + "score": 1.0, + "content": "properties of neural networks. In International Conference on Learning Representations, 2014.", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 213, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 505, + 226 + ], + "score": 1.0, + "content": "C. Szegedy, W. Liu, Y. Jia, P. Sermanet, S. Reed, D. Anguelov, D. Erhan, V. Vanhoucke, and A. Ra-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 115, + 223, + 506, + 238 + ], + "spans": [ + { + "bbox": [ + 115, + 223, + 506, + 238 + ], + "score": 1.0, + "content": "binovich. Going deeper with convolutions. In Computer Vision and Pattern Recognition (CVPR),", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 115, + 235, + 142, + 247 + ], + "spans": [ + { + "bbox": [ + 115, + 235, + 142, + 247 + ], + "score": 1.0, + "content": "2015.", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "M. Gong K. Zhang D. Tao X. Yu, T. Liu. Transfer learning with label noise. ArXiv e-prints, 2017.", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 116, + 265, + 336, + 278 + ], + "spans": [ + { + "bbox": [ + 116, + 265, + 336, + 278 + ], + "score": 1.0, + "content": "URL https://arxiv.org/abs/1707.09724.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 284, + 505, + 297 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 505, + 297 + ], + "score": 1.0, + "content": "Y. Xian, C. H. Lampert, B. Schiele, and Z. Akata. Zero-shot learning - A comprehensive evaluation", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 115, + 295, + 504, + 308 + ], + "spans": [ + { + "bbox": [ + 115, + 295, + 504, + 308 + ], + "score": 1.0, + "content": "of the good, the bad and the ugly. ArXiv e-prints, 2017. URL http://arxiv.org/abs/", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 115, + 306, + 181, + 318 + ], + "spans": [ + { + "bbox": [ + 115, + 306, + 181, + 318 + ], + "score": 1.0, + "content": "1707.00600.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 104, + 324, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 104, + 324, + 506, + 339 + ], + "score": 1.0, + "content": "E. Yudkowsky. Artificial intelligence as a positive and negative factor in global risk. Global catas-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 115, + 336, + 206, + 349 + ], + "spans": [ + { + "bbox": [ + 115, + 336, + 206, + 349 + ], + "score": 1.0, + "content": "trophic risks, 1, 2008.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 355, + 505, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 355, + 505, + 368 + ], + "score": 1.0, + "content": "K. Zhang, B. Scholkopf, K. Muandet, and Z. Wang. Domain adaptation under target and conditional ¨", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 115, + 366, + 370, + 379 + ], + "spans": [ + { + "bbox": [ + 115, + 366, + 370, + 379 + ], + "score": 1.0, + "content": "shift. In International Conference on Machine Learning, 2013.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 384, + 506, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 506, + 398 + ], + "score": 1.0, + "content": "K. Zhang, M. Gong, and B. Scholkopf. Multi-source domain adaptation: A causal view. 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Under Assumption", + "type": "text" + }, + { + "bbox": [ + 239, + 83, + 245, + 92 + ], + "score": 0.27, + "content": "^ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 82, + 316, + 95 + ], + "score": 1.0, + "content": ", with probability", + "type": "text" + }, + { + "bbox": [ + 317, + 83, + 323, + 92 + ], + "score": 0.48, + "content": "^ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "with respect to the training data, the pooled", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 259, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 259, + 106 + ], + "score": 1.0, + "content": "estimator has infinite adversarial loss", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "interline_equation", + "bbox": [ + 267, + 109, + 343, + 125 + ], + "lines": [ + { + "bbox": [ + 267, + 109, + 343, + 125 + ], + "spans": [ + { + "bbox": [ + 267, + 109, + 343, + 125 + ], + "score": 0.91, + "content": "L _ { a d v } ( \\hat { \\theta } ^ { p o o l } ) = \\infty .", + "type": "interline_equation", + "image_path": "718ffe04e002ac06a3d6a1dd25d5b6afb55db56395a81c07603d949ab018a30c.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 267, + 109, + 343, + 125 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 129, + 257, + 141 + ], + "lines": [ + { + "bbox": [ + 106, + 128, + 258, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 128, + 221, + 144 + ], + "score": 1.0, + "content": "For the CORE estimator, for", + "type": "text" + }, + { + "bbox": [ + 221, + 131, + 254, + 140 + ], + "score": 0.85, + "content": "n \\to \\infty", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 128, + 258, + 144 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "interline_equation", + "bbox": [ + 258, + 145, + 352, + 162 + ], + "lines": [ + { + "bbox": [ + 258, + 145, + 352, + 162 + ], + "spans": [ + { + "bbox": [ + 258, + 145, + 352, + 162 + ], + "score": 0.91, + "content": "L _ { a d v } ( \\hat { \\theta } ^ { c o r e } ) _ { p } L _ { a d v } ^ { * } .", + "type": "interline_equation", + "image_path": "7755831fa8a3242b420fd9f542d0fb073c5d7ec985a44cda27d78ebb7a962fd8.jpg" + } + ] + } + ], + "index": 4, + "virtual_lines": [ + { + "bbox": [ + 258, + 145, + 352, + 162 + ], + "spans": [], + "index": 4 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 171, + 504, + 195 + ], + "lines": [ + { + "bbox": [ + 105, + 170, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 505, + 185 + ], + "score": 1.0, + "content": "An equivalent results can be derived for misclassification loss instead of logistic loss (with infinity", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 182, + 169, + 195 + ], + "spans": [ + { + "bbox": [ + 104, + 182, + 169, + 195 + ], + "score": 1.0, + "content": "replaced by 1).", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 106, + 205, + 397, + 218 + ], + "lines": [ + { + "bbox": [ + 105, + 204, + 398, + 221 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 398, + 221 + ], + "score": 1.0, + "content": "Proof. First part. To show the first part, namely that with probability 1,", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "interline_equation", + "bbox": [ + 267, + 222, + 343, + 238 + ], + "lines": [ + { + "bbox": [ + 267, + 222, + 343, + 238 + ], + "spans": [ + { + "bbox": [ + 267, + 222, + 343, + 238 + ], + "score": 0.92, + "content": "L _ { a d v } ( \\hat { \\theta } ^ { p o o l } ) = \\infty ,", + "type": "interline_equation", + "image_path": "c25f70025393060935ac5510809eddadfcd33b82b2acfeae4f800a140ce41347.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 267, + 222, + 343, + 238 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 243, + 506, + 289 + ], + "lines": [ + { + "bbox": [ + 104, + 243, + 507, + 257 + ], + "spans": [ + { + "bbox": [ + 104, + 243, + 194, + 257 + ], + "score": 1.0, + "content": "we need to show that", + "type": "text" + }, + { + "bbox": [ + 194, + 243, + 249, + 256 + ], + "score": 0.92, + "content": "W ^ { t } \\hat { \\theta } ^ { p o o l } \\neq 0", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 243, + 507, + 257 + ], + "score": 1.0, + "content": "with probability 1. 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Under Assumption", + "type": "text" + }, + { + "bbox": [ + 239, + 83, + 245, + 92 + ], + "score": 0.27, + "content": "^ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 245, + 82, + 316, + 95 + ], + "score": 1.0, + "content": ", with probability", + "type": "text" + }, + { + "bbox": [ + 317, + 83, + 323, + 92 + ], + "score": 0.48, + "content": "^ { l }", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "with respect to the training data, the pooled", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 259, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 259, + 106 + ], + "score": 1.0, + "content": "estimator has infinite adversarial loss", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5, + "bbox_fs": [ + 106, + 82, + 505, + 106 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 267, + 109, + 343, + 125 + ], + "lines": [ + { + "bbox": [ + 267, + 109, + 343, + 125 + ], + "spans": [ + { + "bbox": [ + 267, + 109, + 343, + 125 + ], + "score": 0.91, + "content": "L _ { a d v } ( \\hat { \\theta } ^ { p o o l } ) = \\infty .", + "type": "interline_equation", + "image_path": "718ffe04e002ac06a3d6a1dd25d5b6afb55db56395a81c07603d949ab018a30c.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 267, + 109, + 343, + 125 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 129, + 257, + 141 + ], + "lines": [ + { + "bbox": [ + 106, + 128, + 258, + 144 + ], + "spans": [ + { + "bbox": [ + 106, + 128, + 221, + 144 + ], + "score": 1.0, + "content": "For the CORE estimator, for", + "type": "text" + }, + { + "bbox": [ + 221, + 131, + 254, + 140 + ], + "score": 0.85, + "content": "n \\to \\infty", + "type": "inline_equation" + }, + { + "bbox": [ + 254, + 128, + 258, + 144 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3, + "bbox_fs": [ + 106, + 128, + 258, + 144 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 258, + 145, + 352, + 162 + ], + "lines": [ + { + "bbox": [ + 258, + 145, + 352, + 162 + ], + "spans": [ + { + "bbox": [ + 258, + 145, + 352, + 162 + ], + "score": 0.91, + "content": "L _ { a d v } ( \\hat { \\theta } ^ { c o r e } ) _ { p } L _ { a d v } ^ { * } .", + "type": "interline_equation", + "image_path": "7755831fa8a3242b420fd9f542d0fb073c5d7ec985a44cda27d78ebb7a962fd8.jpg" + } + ] + } + ], + "index": 4, + "virtual_lines": [ + { + "bbox": [ + 258, + 145, + 352, + 162 + ], + "spans": [], + "index": 4 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 171, + 504, + 195 + ], + "lines": [ + { + "bbox": [ + 105, + 170, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 505, + 185 + ], + "score": 1.0, + "content": "An equivalent results can be derived for misclassification loss instead of logistic loss (with infinity", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 182, + 169, + 195 + ], + "spans": [ + { + "bbox": [ + 104, + 182, + 169, + 195 + ], + "score": 1.0, + "content": "replaced by 1).", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5, + "bbox_fs": [ + 104, + 170, + 505, + 195 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 205, + 397, + 218 + ], + "lines": [ + { + "bbox": [ + 105, + 204, + 398, + 221 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 398, + 221 + ], + "score": 1.0, + "content": "Proof. First part. To show the first part, namely that with probability 1,", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7, + "bbox_fs": [ + 105, + 204, + 398, + 221 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 267, + 222, + 343, + 238 + ], + "lines": [ + { + "bbox": [ + 267, + 222, + 343, + 238 + ], + "spans": [ + { + "bbox": [ + 267, + 222, + 343, + 238 + ], + "score": 0.92, + "content": "L _ { a d v } ( \\hat { \\theta } ^ { p o o l } ) = \\infty ,", + "type": "interline_equation", + "image_path": "c25f70025393060935ac5510809eddadfcd33b82b2acfeae4f800a140ce41347.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 267, + 222, + 343, + 238 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 243, + 506, + 289 + ], + "lines": [ + { + "bbox": [ + 104, + 243, + 507, + 257 + ], + "spans": [ + { + "bbox": [ + 104, + 243, + 194, + 257 + ], + "score": 1.0, + "content": "we need to show that", + "type": "text" + }, + { + "bbox": [ + 194, + 243, + 249, + 256 + ], + "score": 0.92, + "content": "W ^ { t } \\hat { \\theta } ^ { p o o l } \\neq 0", + "type": "inline_equation" + }, + { + "bbox": [ + 249, + 243, + 507, + 257 + ], + "score": 1.0, + "content": "with probability 1. 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Setting", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 107, + 266, + 504, + 279 + ], + "spans": [ + { + "bbox": [ + 107, + 267, + 145, + 277 + ], + "score": 0.88, + "content": "\\Delta _ { \\kappa } = \\kappa v", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 266, + 160, + 279 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 161, + 267, + 187, + 277 + ], + "score": 0.9, + "content": "\\kappa \\in \\mathbb { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 266, + 219, + 279 + ], + "score": 1.0, + "content": ", we get", + "type": "text" + }, + { + "bbox": [ + 220, + 266, + 342, + 279 + ], + "score": 0.93, + "content": "x ( \\Delta _ { \\kappa } ) ^ { t } \\theta = x ( \\Delta = 0 ) ^ { t } \\theta + \\kappa \\gamma", + "type": "inline_equation" + }, + { + "bbox": [ + 342, + 266, + 373, + 279 + ], + "score": 1.0, + "content": ". 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Note that the invariant space is for this model the linear subspace", + "type": "text" + }, + { + "bbox": [ + 415, + 134, + 501, + 146 + ], + "score": 0.92, + "content": "I = \\{ \\theta : W ^ { t } \\theta = 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 133, + 505, + 146 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 145, + 269, + 158 + ], + "spans": [ + { + "bbox": [ + 106, + 145, + 269, + 158 + ], + "score": 1.0, + "content": "Note that by their respective definitions,", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + }, + { + "type": "interline_equation", + "bbox": [ + 183, + 161, + 427, + 230 + ], + "lines": [ + { + "bbox": [ + 183, + 161, + 427, + 230 + ], + "spans": [ + { + "bbox": [ + 183, + 161, + 427, + 230 + ], + "score": 0.93, + "content": "\\begin{array} { r l r } & { } & { \\hat { \\theta } ^ { * } = \\operatorname * { a r g m i n } _ { \\theta } \\ \\frac { 1 } { m } \\displaystyle \\sum _ { i = 1 } ^ { n } \\sum _ { j = 1 } ^ { m _ { i } } \\ell ( y _ { i } , f _ { \\theta } ( x _ { i , j } ) ) \\ \\mathrm { s u c h \\ t h a t } \\ \\theta \\in I , } \\\\ & { } & { \\hat { \\theta } ^ { c o r e } = \\operatorname * { a r g m i n } _ { \\theta } \\ \\frac { 1 } { m } \\displaystyle \\sum _ { i = 1 } ^ { n } \\sum _ { j = 1 } ^ { m _ { i } } \\ell ( y _ { i } , f _ { \\theta } ( x _ { i , j } ) ) \\ \\mathrm { s u c h \\ t h a t } \\ \\theta \\in I _ { n } . } \\end{array}", + "type": "interline_equation", + "image_path": "a9f713e2b6c818ca0e3f6acec3bbcda68422149dc9578e9f30ab03dfc084604c.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 183, + 161, + 427, + 174.8 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 183, + 174.8, + 427, + 188.60000000000002 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 183, + 188.60000000000002, + 427, + 202.40000000000003 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 183, + 202.40000000000003, + 427, + 216.20000000000005 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 183, + 216.20000000000005, + 427, + 230.00000000000006 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 109, + 234, + 502, + 270 + ], + "lines": [ + { + "bbox": [ + 106, + 234, + 504, + 247 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 263, + 247 + ], + "score": 1.0, + "content": "By (A2) and (A3), with probability 1,", + "type": "text" + }, + { + "bbox": [ + 264, + 234, + 356, + 246 + ], + "score": 0.87, + "content": "I _ { n } = \\{ \\theta : W ^ { t } \\theta = 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 234, + 504, + 247 + ], + "score": 1.0, + "content": "since the number of counterfactuals", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 246, + 504, + 257 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 272, + 257 + ], + "score": 1.0, + "content": "examples is equal to or exceeds the rank", + "type": "text" + }, + { + "bbox": [ + 272, + 248, + 278, + 257 + ], + "score": 0.79, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 246, + 291, + 257 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 291, + 246, + 303, + 255 + ], + "score": 0.83, + "content": "W", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 246, + 321, + 257 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 322, + 246, + 338, + 256 + ], + "score": 0.79, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 246, + 441, + 257 + ], + "score": 1.0, + "content": "has a linear influence on", + "type": "text" + }, + { + "bbox": [ + 441, + 246, + 451, + 255 + ], + "score": 0.82, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 246, + 504, + 257 + ], + "score": 1.0, + "content": ". Hence with", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 257, + 428, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 257, + 198, + 271 + ], + "score": 1.0, + "content": "probability 1, we have", + "type": "text" + }, + { + "bbox": [ + 198, + 258, + 227, + 270 + ], + "score": 0.92, + "content": "I = I _ { n }", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 257, + 271, + 271 + ], + "score": 1.0, + "content": "and hence", + "type": "text" + }, + { + "bbox": [ + 271, + 257, + 315, + 268 + ], + "score": 0.91, + "content": "\\hat { \\theta } ^ { c o r e } = \\hat { \\theta } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 316, + 257, + 428, + 271 + ], + "score": 1.0, + "content": ". We thus need to show that", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12 + }, + { + "type": "interline_equation", + "bbox": [ + 264, + 274, + 347, + 290 + ], + "lines": [ + { + "bbox": [ + 264, + 274, + 347, + 290 + ], + "spans": [ + { + "bbox": [ + 264, + 274, + 347, + 290 + ], + "score": 0.92, + "content": "L _ { a d v } ( \\hat { \\theta } ^ { * } ) _ { p } L _ { a d v } ^ { * } .", + "type": "interline_equation", + "image_path": "11ed3a5ce402da7f0b3abc8086efb889bfcac6af38e201dcf8825d558a705901.jpg" + } + ] + } + ], + "index": 14, + "virtual_lines": [ + { + "bbox": [ + 264, + 274, + 347, + 290 + ], + "spans": [], + "index": 14 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 296, + 505, + 319 + ], + "lines": [ + { + "bbox": [ + 106, + 294, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 131, + 310 + ], + "score": 1.0, + "content": "Since", + "type": "text" + }, + { + "bbox": [ + 131, + 295, + 141, + 307 + ], + "score": 0.87, + "content": "{ \\hat { \\theta } } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 142, + 294, + 162, + 310 + ], + "score": 1.0, + "content": "is in", + "type": "text" + }, + { + "bbox": [ + 162, + 297, + 168, + 307 + ], + "score": 0.76, + "content": "I", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 294, + 207, + 310 + ], + "score": 1.0, + "content": ", we have", + "type": "text" + }, + { + "bbox": [ + 207, + 296, + 304, + 309 + ], + "score": 0.91, + "content": "\\ell ( y , x ( \\Delta ) ) = \\ell ( y , x ( 0 ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 294, + 335, + 310 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 335, + 297, + 354, + 309 + ], + "score": 0.92, + "content": "x ( 0 )", + "type": "inline_equation" + }, + { + "bbox": [ + 355, + 294, + 505, + 310 + ], + "score": 1.0, + "content": "are the previously discussed counter-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 308, + 311, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 311, + 320 + ], + "score": 1.0, + "content": "factual data in the absence of interventions. Hence", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5 + }, + { + "type": "interline_equation", + "bbox": [ + 185, + 321, + 426, + 356 + ], + "lines": [ + { + "bbox": [ + 185, + 321, + 426, + 356 + ], + "spans": [ + { + "bbox": [ + 185, + 321, + 426, + 356 + ], + "score": 0.92, + "content": "\\hat { \\theta } ^ { * } = \\operatorname * { a r g m i n } _ { \\theta } \\ \\frac { 1 } { m } \\sum _ { i = 1 } ^ { n } \\sum _ { j = 1 } ^ { m _ { i } } \\ell ( y _ { i } , f _ { \\theta } ( x _ { i , j } ( 0 ) ) ) \\ \\mathrm { s u c h ~ t h a t } \\theta \\in I ,", + "type": "interline_equation", + "image_path": "80e18f519dd16fa4dd3b09fc077a4b091564c3747e478b4316ae77521b4c5cf5.jpg" + } + ] + } + ], + "index": 17.5, + "virtual_lines": [ + { + "bbox": [ + 185, + 321, + 426, + 338.5 + ], + "spans": [], + "index": 17 + }, + { + "bbox": [ + 185, + 338.5, + 426, + 356.0 + ], + "spans": [], + "index": 18 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 359, + 504, + 382 + ], 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This completes the proof, using the previous fact that", + "type": "text" + }, + { + "bbox": [ + 399, + 585, + 444, + 597 + ], + "score": 0.92, + "content": "\\hat { \\theta } ^ { c o r e } = \\hat { \\theta } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 583, + 507, + 603 + ], + "score": 1.0, + "content": "with probabil-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 598, + 177, + 611 + ], + "spans": [ + { + "bbox": [ + 106, + 598, + 177, + 611 + ], + "score": 1.0, + "content": "ity 1 under (A3).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32.5 + }, + { + "type": "title", + "bbox": [ + 108, + 642, + 270, + 655 + ], + "lines": [ + { + "bbox": [ + 105, + 641, + 272, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 272, + 657 + ], + "score": 1.0, + "content": "B ADDITIONAL EXPERIMENTS", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "title", + "bbox": [ + 107, + 667, + 243, + 678 + ], + "lines": [ + { + "bbox": [ + 106, + 666, + 244, + 680 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 244, + 680 + ], + "score": 1.0, + "content": "B.1 GENDER CLASSIFICATION", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "We work with the CelebA dataset (Liu et al., 2015) and consider the problem of classifying whether", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "the person in the image is male or female. We create a confounding by including mostly images", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "of men wearing glasses while the images of women do not include photos of women with glasses.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "As counterfactuals, we use an image of the same person without glasses if the person is male and", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38.5 + } + ], + "page_idx": 17, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 26, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 309, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 309, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 763 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 763 + ], + "score": 1.0, + "content": "18", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 494, + 615, + 505, + 625 + ], + "lines": [ + { + "bbox": [ + 495, + 617, + 505, + 626 + ], + "spans": [ + { + "bbox": [ + 495, + 617, + 505, + 626 + ], + "score": 0.999, + "content": "□", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 116 + ], + "lines": [], + "index": 1, + "bbox_fs": [ + 105, + 82, + 506, + 117 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 122, + 505, + 157 + ], + "lines": [ + { + "bbox": [ + 105, + 121, + 505, + 135 + ], + "spans": [ + { + "bbox": [ + 105, + 122, + 394, + 135 + ], + "score": 1.0, + "content": "Second part. 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Note that the invariant space is for this model the linear subspace", + "type": "text" + }, + { + "bbox": [ + 415, + 134, + 501, + 146 + ], + "score": 0.92, + "content": "I = \\{ \\theta : W ^ { t } \\theta = 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 133, + 505, + 146 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 145, + 269, + 158 + ], + "spans": [ + { + "bbox": [ + 106, + 145, + 269, + 158 + ], + "score": 1.0, + "content": "Note that by their respective definitions,", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4, + "bbox_fs": [ + 105, + 121, + 505, + 158 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 183, + 161, + 427, + 230 + ], + "lines": [ + { + "bbox": [ + 183, + 161, + 427, + 230 + ], + "spans": [ + { + "bbox": [ + 183, + 161, + 427, + 230 + ], + "score": 0.93, + "content": "\\begin{array} { r l r } & { } & { \\hat { \\theta } ^ { * } = \\operatorname * { a r g m i n } _ { \\theta } \\ \\frac { 1 } { m } \\displaystyle \\sum _ { i = 1 } ^ { n } \\sum _ { j = 1 } ^ { m _ { i } } \\ell ( y _ { i } , f _ { \\theta } ( x _ { i , j } ) ) \\ \\mathrm { s u c h \\ t h a t } \\ \\theta \\in I , } \\\\ & { } & { \\hat { \\theta } ^ { c o r e } = \\operatorname * { a r g m i n } _ { \\theta } \\ \\frac { 1 } { m } \\displaystyle \\sum _ { i = 1 } ^ { n } \\sum _ { j = 1 } ^ { m _ { i } } \\ell ( y _ { i } , f _ { \\theta } ( x _ { i , j } ) ) \\ \\mathrm { s u c h \\ t h a t } \\ \\theta \\in I _ { n } . } \\end{array}", + "type": "interline_equation", + "image_path": "a9f713e2b6c818ca0e3f6acec3bbcda68422149dc9578e9f30ab03dfc084604c.jpg" + } + ] + } + ], + "index": 8, + "virtual_lines": [ + { + "bbox": [ + 183, + 161, + 427, + 174.8 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 183, + 174.8, + 427, + 188.60000000000002 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 183, + 188.60000000000002, + 427, + 202.40000000000003 + ], + "spans": [], + "index": 8 + }, + { + "bbox": [ + 183, + 202.40000000000003, + 427, + 216.20000000000005 + ], + "spans": [], + "index": 9 + }, + { + "bbox": [ + 183, + 216.20000000000005, + 427, + 230.00000000000006 + ], + "spans": [], + "index": 10 + } + ] + }, + { + "type": "text", + "bbox": [ + 109, + 234, + 502, + 270 + ], + "lines": [ + { + "bbox": [ + 106, + 234, + 504, + 247 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 263, + 247 + ], + "score": 1.0, + "content": "By (A2) and (A3), with probability 1,", + "type": "text" + }, + { + "bbox": [ + 264, + 234, + 356, + 246 + ], + "score": 0.87, + "content": "I _ { n } = \\{ \\theta : W ^ { t } \\theta = 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 234, + 504, + 247 + ], + "score": 1.0, + "content": "since the number of counterfactuals", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 246, + 504, + 257 + ], + "spans": [ + { + "bbox": [ + 106, + 246, + 272, + 257 + ], + "score": 1.0, + "content": "examples is equal to or exceeds the rank", + "type": "text" + }, + { + "bbox": [ + 272, + 248, + 278, + 257 + ], + "score": 0.79, + "content": "q", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 246, + 291, + 257 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 291, + 246, + 303, + 255 + ], + "score": 0.83, + "content": "W", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 246, + 321, + 257 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 322, + 246, + 338, + 256 + ], + "score": 0.79, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 339, + 246, + 441, + 257 + ], + "score": 1.0, + "content": "has a linear influence on", + "type": "text" + }, + { + "bbox": [ + 441, + 246, + 451, + 255 + ], + "score": 0.82, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 246, + 504, + 257 + ], + "score": 1.0, + "content": ". 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Hence", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5, + "bbox_fs": [ + 106, + 294, + 505, + 320 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 185, + 321, + 426, + 356 + ], + "lines": [ + { + "bbox": [ + 185, + 321, + 426, + 356 + ], + "spans": [ + { + "bbox": [ + 185, + 321, + 426, + 356 + ], + "score": 0.92, + "content": "\\hat { \\theta } ^ { * } = \\operatorname * { a r g m i n } _ { \\theta } \\ \\frac { 1 } { m } \\sum _ { i = 1 } ^ { n } \\sum _ { j = 1 } ^ { m _ { i } } \\ell ( y _ { i } , f _ { \\theta } ( x _ { i , j } ( 0 ) ) ) \\ \\mathrm { s u c h ~ t h a t } \\theta \\in I ,", + "type": "interline_equation", + "image_path": "80e18f519dd16fa4dd3b09fc077a4b091564c3747e478b4316ae77521b4c5cf5.jpg" + } + ] + } + ], + "index": 17.5, + "virtual_lines": [ + { + "bbox": [ + 185, + 321, + 426, + 338.5 + ], + "spans": [], + "index": 17 + }, + { + "bbox": [ + 185, + 338.5, + 426, + 356.0 + ], + "spans": [], + "index": 18 + } + ] + }, + { + "type": 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Here we analyze a confounded setting that could arise", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 466, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 288, + 480 + ], + "score": 1.0, + "content": "as follows. Say the hidden common cause of", + "type": "text" + }, + { + "bbox": [ + 289, + 467, + 298, + 477 + ], + "score": 0.78, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 298, + 466, + 316, + 480 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 316, + 466, + 333, + 477 + ], + "score": 0.86, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 466, + 337, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 337, + 467, + 347, + 477 + ], + "score": 0.76, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 466, + 506, + 480 + ], + "score": 1.0, + "content": "indicates whether the image was taken", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 478, + 505, + 490 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 505, + 490 + ], + "score": 1.0, + "content": "outdoors or indoors. If it was taken outdoors, then the person wears glasses and the image tends to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 487, + 506, + 503 + ], + "spans": [ + { + "bbox": [ + 104, + 487, + 506, + 503 + ], + "score": 1.0, + "content": "be brighter. If the image was taken indoors, then the person does not wear glasses and the image", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 499, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 244, + 513 + ], + "score": 1.0, + "content": "tends to be darker. In other words,", + "type": "text" + }, + { + "bbox": [ + 244, + 499, + 274, + 510 + ], + "score": 0.68, + "content": "X ^ { \\perp } \\equiv .", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "brightness and the structure of the data generating process", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 510, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 505, + 524 + ], + "score": 1.0, + "content": "is equivalent to the one shown in Figure C.9. Figure B.3a shows examples from the training set.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 522, + 506, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 534 + ], + "score": 1.0, + "content": "Here, we use as the counterfactual observation the same image (CF setting 1) but with a different", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "score": 1.0, + "content": "brightness. Two alternatives for constructing counterfactual observations in this setting are discussed", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 544, + 288, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 117, + 556 + ], + "score": 1.0, + "content": "in", + "type": "text" + }, + { + "bbox": [ + 117, + 544, + 144, + 556 + ], + "score": 0.83, + "content": "\\ S \\mathbf { B } . 2 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 544, + 179, + 556 + ], + "score": 1.0, + "content": ". We use", + "type": "text" + }, + { + "bbox": [ + 180, + 544, + 219, + 554 + ], + "score": 0.87, + "content": "c = 2 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 544, + 236, + 556 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 236, + 544, + 285, + 554 + ], + "score": 0.88, + "content": "m = 2 0 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 544, + 288, + 556 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 30.5 + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 638 + ], + "lines": [ + { + "bbox": [ + 105, + 560, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 505, + 573 + ], + "score": 1.0, + "content": "For the brightness intervention, we sample the value for the magnitude of the brightness increase", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 339, + 585 + ], + "score": 1.0, + "content": "resp. decrease from an exponential distribution with mean", + "type": "text" + }, + { + "bbox": [ + 340, + 572, + 370, + 583 + ], + "score": 0.9, + "content": "\\beta = 2 0", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 572, + 505, + 585 + ], + "score": 1.0, + "content": ". Specifically, we use ImageMag-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 580, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 124, + 593 + ], + "score": 0.7, + "content": "\\mathrm { i c k } ^ { \\mathrm { \\scriptsize 9 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 124, + 580, + 505, + 597 + ], + "score": 1.0, + "content": "to modify the brightness of each image. In the training set and test set 1, we sample the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 593, + 506, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 186, + 607 + ], + "score": 1.0, + "content": "brightness value as", + "type": "text" + }, + { + "bbox": [ + 186, + 594, + 266, + 606 + ], + "score": 0.91, + "content": "b _ { i , j } = 1 0 0 + y _ { i } e _ { i , j }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 593, + 295, + 607 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 296, + 593, + 366, + 606 + ], + "score": 0.92, + "content": "e _ { i , j } \\sim E x p ( \\beta ^ { - \\bar { 1 } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 593, + 385, + 607 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 386, + 594, + 441, + 606 + ], + "score": 0.92, + "content": "y _ { i } \\in \\{ - 1 , 1 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 441, + 593, + 447, + 607 + ], + "score": 1.0, + "content": ".", + "type": "text" + }, + { + "bbox": [ + 447, + 594, + 477, + 605 + ], + "score": 0.89, + "content": "y _ { i } = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 478, + 593, + 506, + 607 + ], + "score": 1.0, + "content": "corre-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 604, + 504, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 147, + 618 + ], + "score": 1.0, + "content": "sponds to", + "type": "text" + }, + { + "bbox": [ + 147, + 605, + 201, + 616 + ], + "score": 0.83, + "content": "y _ { i } \\equiv g l a s s e s", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 604, + 460, + 618 + ], + "score": 1.0, + "content": ". We then apply the command convert -modulate b ij,", + "type": "text" + }, + { + "bbox": [ + 461, + 605, + 504, + 616 + ], + "score": 0.34, + "content": "^ { 1 0 0 , 1 0 0 }", + "type": "inline_equation" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "input.jpg output.jpg to the image. Importantly, since we sample from an exponential dis-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 627, + 502, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 502, + 639 + ], + "score": 1.0, + "content": "tribution, the brightness interventions are quite subtle in many cases as can be seen in Figure B.3a.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 710 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "score": 1.0, + "content": "Figure B.3c shows misclassification rates for CORE and the pooled estimator on different test sets.", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "score": 1.0, + "content": "Examples from all test sets can be found in Figure B.4. Test set 1 follows the same distribution as", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "the training set. In test set 2 the sign of the brightness intervention is reversed, i.e. images of people", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 676, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 506, + 689 + ], + "score": 1.0, + "content": "with glasses tend to be darker; images of people without glasses tend to be brighter. In test set 3", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "score": 1.0, + "content": "all images are left unchanged and in test set 4 the brightness of all images is increased. First, we", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "score": 1.0, + "content": "notice that the pooled estimator performs better than CORE on test set 1. 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Figure B.2 shows the results for varying numbers of", + "type": "text" + }, + { + "bbox": [ + 450, + 333, + 460, + 341 + ], + "score": 0.74, + "content": "m", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 331, + 480, + 343 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 480, + 333, + 486, + 342 + ], + "score": 0.63, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 331, + 505, + 343 + ], + "score": 1.0, + "content": "—in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 340, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 104, + 340, + 505, + 356 + ], + "score": 1.0, + "content": "the left column for training a four-layer CNN; in the right column for using Inception V3 features.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 352, + 505, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 352, + 251, + 366 + ], + "score": 1.0, + "content": "Overall, we see the same trends: As", + "type": "text" + }, + { + "bbox": [ + 252, + 355, + 258, + 363 + ], + "score": 0.66, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 258, + 352, + 505, + 366 + ], + "score": 1.0, + "content": "increases, the performance difference between CORE and the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 363, + 504, + 377 + ], + "spans": [ + { + "bbox": [ + 106, + 363, + 362, + 377 + ], + "score": 1.0, + "content": "pooled estimator becomes smaller. This is due to the fact that", + "type": "text" + }, + { + "bbox": [ + 363, + 364, + 380, + 375 + ], + "score": 0.9, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 380, + 363, + 504, + 377 + ], + "score": 1.0, + "content": "is binary in this example and,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 375, + 504, + 387 + ], + "spans": [ + { + "bbox": [ + 106, + 375, + 504, + 387 + ], + "score": 1.0, + "content": "therefore, including counterfactual examples corresponds to data augmentation. Interestingly, the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 385, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 302, + 399 + ], + "score": 1.0, + "content": "pooled estimator performs worse on test set 2 as", + "type": "text" + }, + { + "bbox": [ + 303, + 388, + 313, + 396 + ], + "score": 0.69, + "content": "m", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 385, + 476, + 399 + ], + "score": 1.0, + "content": "becomes larger. It thus seems to exploit", + "type": "text" + }, + { + "bbox": [ + 477, + 385, + 493, + 396 + ], + "score": 0.89, + "content": "\\dot { X } ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 493, + 385, + 506, + 399 + ], + "score": 1.0, + "content": "to", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 397, + 217, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 176, + 410 + ], + "score": 1.0, + "content": "a larger extent as", + "type": "text" + }, + { + "bbox": [ + 176, + 399, + 187, + 407 + ], + "score": 0.68, + "content": "m", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 397, + 217, + 410 + ], + "score": 1.0, + "content": "grows.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 20, + "bbox_fs": [ + 104, + 309, + 506, + 410 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 424, + 370, + 435 + ], + "lines": [ + { + "bbox": [ + 106, + 424, + 371, + 436 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 371, + 436 + ], + "score": 1.0, + "content": "B.2 EYEGLASSES DETECTION: BRIGHTNESS INTERVENTION", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 505, + 555 + ], + "lines": [ + { + "bbox": [ + 106, + 446, + 504, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 446, + 131, + 457 + ], + "score": 1.0, + "content": "As in", + "type": "text" + }, + { + "bbox": [ + 132, + 446, + 150, + 457 + ], + "score": 0.57, + "content": "\\ S 5 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 151, + 446, + 504, + 457 + ], + "score": 1.0, + "content": "we work with the CelebA dataset and consider the problem of classifying whether the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 456, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 506, + 469 + ], + "score": 1.0, + "content": "person in the image is wearing eyeglasses. Here we analyze a confounded setting that could arise", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 466, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 288, + 480 + ], + "score": 1.0, + "content": "as follows. Say the hidden common cause of", + "type": "text" + }, + { + "bbox": [ + 289, + 467, + 298, + 477 + ], + "score": 0.78, + "content": "Y", + "type": "inline_equation" + }, + { + "bbox": [ + 298, + 466, + 316, + 480 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 316, + 466, + 333, + 477 + ], + "score": 0.86, + "content": "X ^ { \\perp }", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 466, + 337, + 480 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 337, + 467, + 347, + 477 + ], + "score": 0.76, + "content": "D", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 466, + 506, + 480 + ], + "score": 1.0, + "content": "indicates whether the image was taken", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 478, + 505, + 490 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 505, + 490 + ], + "score": 1.0, + "content": "outdoors or indoors. If it was taken outdoors, then the person wears glasses and the image tends to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 487, + 506, + 503 + ], + "spans": [ + { + "bbox": [ + 104, + 487, + 506, + 503 + ], + "score": 1.0, + "content": "be brighter. If the image was taken indoors, then the person does not wear glasses and the image", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 499, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 244, + 513 + ], + "score": 1.0, + "content": "tends to be darker. In other words,", + "type": "text" + }, + { + "bbox": [ + 244, + 499, + 274, + 510 + ], + "score": 0.68, + "content": "X ^ { \\perp } \\equiv .", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 500, + 505, + 513 + ], + "score": 1.0, + "content": "brightness and the structure of the data generating process", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 510, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 510, + 505, + 524 + ], + "score": 1.0, + "content": "is equivalent to the one shown in Figure C.9. Figure B.3a shows examples from the training set.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 522, + 506, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 506, + 534 + ], + "score": 1.0, + "content": "Here, we use as the counterfactual observation the same image (CF setting 1) but with a different", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 505, + 545 + ], + "score": 1.0, + "content": "brightness. Two alternatives for constructing counterfactual observations in this setting are discussed", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 544, + 288, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 544, + 117, + 556 + ], + "score": 1.0, + "content": "in", + "type": "text" + }, + { + "bbox": [ + 117, + 544, + 144, + 556 + ], + "score": 0.83, + "content": "\\ S \\mathbf { B } . 2 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 144, + 544, + 179, + 556 + ], + "score": 1.0, + "content": ". We use", + "type": "text" + }, + { + "bbox": [ + 180, + 544, + 219, + 554 + ], + "score": 0.87, + "content": "c = 2 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 544, + 236, + 556 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 236, + 544, + 285, + 554 + ], + "score": 0.88, + "content": "m = 2 0 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 285, + 544, + 288, + 556 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 30.5, + "bbox_fs": [ + 104, + 446, + 506, + 556 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 561, + 505, + 638 + ], + "lines": [ + { + "bbox": [ + 105, + 560, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 505, + 573 + ], + "score": 1.0, + "content": "For the brightness intervention, we sample the value for the magnitude of the brightness increase", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 339, + 585 + ], + "score": 1.0, + "content": "resp. decrease from an exponential distribution with mean", + "type": "text" + }, + { + "bbox": [ + 340, + 572, + 370, + 583 + ], + "score": 0.9, + "content": "\\beta = 2 0", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 572, + 505, + 585 + ], + "score": 1.0, + "content": ". Specifically, we use ImageMag-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 580, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 124, + 593 + ], + "score": 0.7, + "content": "\\mathrm { i c k } ^ { \\mathrm { \\scriptsize 9 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 124, + 580, + 505, + 597 + ], + "score": 1.0, + "content": "to modify the brightness of each image. In the training set and test set 1, we sample the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 593, + 506, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 186, + 607 + ], + "score": 1.0, + "content": "brightness value as", + "type": "text" + }, + { + "bbox": [ + 186, + 594, + 266, + 606 + ], + "score": 0.91, + "content": "b _ { i , j } = 1 0 0 + y _ { i } e _ { i , j }", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 593, + 295, + 607 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 296, + 593, + 366, + 606 + ], + "score": 0.92, + "content": "e _ { i , j } \\sim E x p ( \\beta ^ { - \\bar { 1 } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 593, + 385, + 607 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 386, + 594, + 441, + 606 + ], + "score": 0.92, + "content": "y _ { i } \\in \\{ - 1 , 1 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 441, + 593, + 447, + 607 + ], + "score": 1.0, + "content": ".", + "type": "text" + }, + { + "bbox": [ + 447, + 594, + 477, + 605 + ], + "score": 0.89, + "content": "y _ { i } = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 478, + 593, + 506, + 607 + ], + "score": 1.0, + "content": "corre-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 604, + 504, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 147, + 618 + ], + "score": 1.0, + "content": "sponds to", + "type": "text" + }, + { + "bbox": [ + 147, + 605, + 201, + 616 + ], + "score": 0.83, + "content": "y _ { i } \\equiv g l a s s e s", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 604, + 460, + 618 + ], + "score": 1.0, + "content": ". We then apply the command convert -modulate b ij,", + "type": "text" + }, + { + "bbox": [ + 461, + 605, + 504, + 616 + ], + "score": 0.34, + "content": "^ { 1 0 0 , 1 0 0 }", + "type": "inline_equation" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "input.jpg output.jpg to the image. Importantly, since we sample from an exponential dis-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 627, + 502, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 502, + 639 + ], + "score": 1.0, + "content": "tribution, the brightness interventions are quite subtle in many cases as can be seen in Figure B.3a.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 560, + 506, + 639 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 643, + 505, + 710 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 656 + ], + "score": 1.0, + "content": "Figure B.3c shows misclassification rates for CORE and the pooled estimator on different test sets.", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 666 + ], + "score": 1.0, + "content": "Examples from all test sets can be found in Figure B.4. Test set 1 follows the same distribution as", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "the training set. In test set 2 the sign of the brightness intervention is reversed, i.e. images of people", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 676, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 676, + 506, + 689 + ], + "score": 1.0, + "content": "with glasses tend to be darker; images of people without glasses tend to be brighter. In test set 3", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "score": 1.0, + "content": "all images are left unchanged and in test set 4 the brightness of all images is increased. First, we", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 711 + ], + "score": 1.0, + "content": "notice that the pooled estimator performs better than CORE on test set 1. This can be explained by", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 290, + 504, + 301 + ], + "spans": [ + { + "bbox": [ + 106, + 290, + 504, + 301 + ], + "score": 1.0, + "content": "the fact that it can exploit the predictive information contained in the brightness of an image while", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 300, + 505, + 313 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 505, + 313 + ], + "score": 1.0, + "content": "CORE is restricted not to do so. Second, we observe that the pooled estimator does not perform well", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 312, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 505, + 324 + ], + "score": 1.0, + "content": "on test sets 2 and 4 as its learned representation seems to use the image’s brightness as a predictor", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 321, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 505, + 336 + ], + "score": 1.0, + "content": "for the response which fails when the brightness distribution in the test set differs significantly", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 333, + 505, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 505, + 346 + ], + "score": 1.0, + "content": "from the training set. In contrast, the predictive performance of CORE is hardly affected by the", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 290, + 357 + ], + "score": 1.0, + "content": "changing brightness distributions. 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The first three images from the left have", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 235, + 505, + 248 + ], + "spans": [ + { + "bbox": [ + 107, + 237, + 134, + 246 + ], + "score": 0.87, + "content": "y \\equiv n o", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 235, + 284, + 248 + ], + "score": 1.0, + "content": "glasses; the remaining three images have", + "type": "text" + }, + { + "bbox": [ + 284, + 236, + 328, + 246 + ], + "score": 0.73, + "content": "y \\equiv g l a s s e s", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 235, + 505, + 248 + ], + "score": 1.0, + "content": ". 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Second, we observe that the pooled estimator does not perform well", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 312, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 505, + 324 + ], + "score": 1.0, + "content": "on test sets 2 and 4 as its learned representation seems to use the image’s brightness as a predictor", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 321, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 505, + 336 + ], + "score": 1.0, + "content": "for the response which fails when the brightness distribution in the test set differs significantly", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 333, + 505, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 505, + 346 + ], + "score": 1.0, + "content": "from the training set. In contrast, the predictive performance of CORE is hardly affected by the", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 344, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 290, + 357 + ], + "score": 1.0, + "content": "changing brightness distributions. Results for", + "type": "text" + }, + { + "bbox": [ + 291, + 344, + 354, + 357 + ], + "score": 0.94, + "content": "\\beta \\in \\{ 5 , 1 0 , 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 354, + 344, + 372, + 357 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 372, + 344, + 439, + 357 + ], + "score": 0.93, + "content": "c \\in \\{ 2 0 0 , 5 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 344, + 505, + 357 + ], + "score": 1.0, + "content": "can be found in", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 354, + 155, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 155, + 369 + ], + "score": 1.0, + "content": "Figure B.5.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 10 + }, + { + "type": "title", + "bbox": [ + 108, + 380, + 304, + 392 + ], + "lines": [ + { + "bbox": [ + 105, + 380, + 306, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 306, + 393 + ], + "score": 1.0, + "content": "B.2.1 COUNTERFACTUAL SETTINGS 2 AND 3", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 400, + 505, + 456 + ], + "lines": [ + { + "bbox": [ + 106, + 400, + 504, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 400, + 504, + 412 + ], + "score": 1.0, + "content": "Above we used the same image to create a counterfactual observation by sampling a different value", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 411, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 505, + 424 + ], + "score": 1.0, + "content": "for the brightness intervention. A plausible alternative is to use a different image of the same person", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 422, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 279, + 436 + ], + "score": 1.0, + "content": "as counterfactual. We call this “CF setting", + "type": "text" + }, + { + "bbox": [ + 279, + 423, + 289, + 433 + ], + "score": 0.39, + "content": "2 ^ { \\circ }", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 422, + 505, + 436 + ], + "score": 1.0, + "content": ". For comparison, we also evaluate using an image of", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 432, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 355, + 447 + ], + "score": 1.0, + "content": "a different person as counterfactual as a baseline (“CF setting", + "type": "text" + }, + { + "bbox": [ + 356, + 434, + 367, + 444 + ], + "score": 0.37, + "content": "3 ^ { \\circ }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 432, + 505, + 447 + ], + "score": 1.0, + "content": "). Examples from the training sets", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 444, + 318, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 318, + 457 + ], + "score": 1.0, + "content": "using CF setting 2 and 3 can be found in Figure B.4.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 461, + 505, + 528 + ], + "lines": [ + { + "bbox": [ + 105, + 460, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 263, + 474 + ], + "score": 1.0, + "content": "Results for all counterfactual settings,", + "type": "text" + }, + { + "bbox": [ + 263, + 461, + 329, + 474 + ], + "score": 0.93, + "content": "\\beta \\in \\{ 5 , 1 0 , 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 460, + 348, + 474 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 348, + 461, + 417, + 474 + ], + "score": 0.92, + "content": "c \\in \\{ 2 0 0 , 5 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 460, + 505, + 474 + ], + "score": 1.0, + "content": "can be found in Fig-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "score": 1.0, + "content": "ure B.5. We see that using counterfactual setting 1 works best since we could explicitly control", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 482, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 146, + 497 + ], + "score": 1.0, + "content": "that only", + "type": "text" + }, + { + "bbox": [ + 146, + 483, + 177, + 494 + ], + "score": 0.64, + "content": "X ^ { \\perp } \\equiv", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 482, + 506, + 497 + ], + "score": 1.0, + "content": "brightness varies between counterfactual examples. In counterfactual setting 2,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 493, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 506, + 507 + ], + "score": 1.0, + "content": "different images of the same person can vary in many factors, making it more challenging to isolate", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "brightness as the factor to be invariant against. Lastly, we see that even grouping images of different", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 516, + 353, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 353, + 530 + ], + "score": 1.0, + "content": "persons can still help predictive performance to some degree.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5 + }, + { + "type": "title", + "bbox": [ + 107, + 546, + 495, + 573 + ], + "lines": [ + { + "bbox": [ + 105, + 545, + 497, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 497, + 560 + ], + "score": 1.0, + "content": "C EXPERIMENTAL DETAILS AND ADDITIONAL RESULTS FOR EXPERIMENTS", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 126, + 559, + 267, + 574 + ], + "spans": [ + { + "bbox": [ + 126, + 559, + 267, + 574 + ], + "score": 1.0, + "content": "INTRODUCED IN §2 AND §5", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26.5 + }, + { + "type": "title", + "bbox": [ + 108, + 585, + 298, + 596 + ], + "lines": [ + { + "bbox": [ + 106, + 585, + 298, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 290, + 598 + ], + "score": 1.0, + "content": "C.1 CHOOSING THE TUNING PARAMETER", + "type": "text" + }, + { + "bbox": [ + 291, + 586, + 298, + 595 + ], + "score": 0.46, + "content": "\\lambda", + "type": "inline_equation" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 606, + 505, + 651 + ], + "lines": [ + { + "bbox": [ + 105, + 606, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 375, + 619 + ], + "score": 1.0, + "content": "An open question is how to set the value of the tuning parameter", + "type": "text" + }, + { + "bbox": [ + 375, + 609, + 382, + 617 + ], + "score": 0.75, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 606, + 486, + 619 + ], + "score": 1.0, + "content": "in Eq. (4) or the penalty", + "type": "text" + }, + { + "bbox": [ + 486, + 607, + 493, + 617 + ], + "score": 0.78, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 493, + 606, + 505, + 619 + ], + "score": 1.0, + "content": "in", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 618, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 505, + 630 + ], + "score": 1.0, + "content": "the Lagrangian form. Figure C.6 shows the misclassification rates of CORE on the subsampled", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 343, + 642 + ], + "score": 1.0, + "content": "and augmented AwA2 dataset as a function of the penalty", + "type": "text" + }, + { + "bbox": [ + 344, + 629, + 351, + 639 + ], + "score": 0.72, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 628, + 505, + 642 + ], + "score": 1.0, + "content": ". We see that performance is not very", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 640, + 218, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 207, + 651 + ], + "score": 1.0, + "content": "sensitive to the choice of", + "type": "text" + }, + { + "bbox": [ + 208, + 640, + 215, + 650 + ], + "score": 0.75, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 640, + 218, + 651 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5 + }, + { + "type": "title", + "bbox": [ + 106, + 666, + 471, + 678 + ], + "lines": [ + { + "bbox": [ + 115, + 666, + 462, + 678 + ], + "spans": [ + { + "bbox": [ + 115, + 666, + 462, + 678 + ], + "score": 1.0, + "content": ".2 GROUPING PHOTOS OF THE SAME PERSON: BETTER PREDICTIVE PERFORMAN", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 108, + 687, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 359, + 700 + ], + "score": 1.0, + "content": "Here, we show further results for the experiment introduced in", + "type": "text" + }, + { + "bbox": [ + 359, + 688, + 377, + 699 + ], + "score": 0.82, + "content": "\\ S 2 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 687, + 505, + 700 + ], + "score": 1.0, + "content": ". We vary the number of identi-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 699, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 252, + 711 + ], + "score": 1.0, + "content": "ties included in the training data set", + "type": "text" + }, + { + "bbox": [ + 253, + 699, + 355, + 711 + ], + "score": 0.9, + "content": "n \\in \\{ 1 0 , 2 0 , 4 0 , 8 0 , 1 6 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 699, + 494, + 711 + ], + "score": 1.0, + "content": ". This results in total sample sizes", + "type": "text" + }, + { + "bbox": [ + 494, + 701, + 504, + 709 + ], + "score": 0.5, + "content": "m", + "type": "inline_equation" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 195, + 722 + ], + "score": 1.0, + "content": "ranging from 321 for", + "type": "text" + }, + { + "bbox": [ + 195, + 710, + 227, + 720 + ], + "score": 0.9, + "content": "n = 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 710, + 277, + 722 + ], + "score": 1.0, + "content": "to 4386 for", + "type": "text" + }, + { + "bbox": [ + 277, + 711, + 315, + 720 + ], + "score": 0.88, + "content": "n = 1 6 0", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 710, + 505, + 722 + ], + "score": 1.0, + "content": ", implying that the average number of counter-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 371, + 733 + ], + "score": 1.0, + "content": "factual observations per person varies between 27 and 32. Figure", + "type": "text" + }, + { + "bbox": [ + 372, + 721, + 393, + 731 + ], + "score": 0.28, + "content": "{ \\mathrm { C . 7 b } }", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "shows the misclassification", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35.5 + } + ], + "page_idx": 20, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 309, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 309, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 298, + 750, + 312, + 765 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 312, + 765 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 15, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 117, + 78, + 504, + 221 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 117, + 78, + 504, + 221 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 117, + 78, + 504, + 221 + ], + "spans": [ + { + "bbox": [ + 117, + 78, + 504, + 221 + ], + "score": 0.949, + "type": "image", + "image_path": "d16e6f39caf4bbec0a6a5f5d4cc670f751d20a0a246893e2e34dc69efaf115c2.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 117, + 78, + 504, + 125.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 117, + 125.66666666666666, + 504, + 173.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 117, + 173.33333333333331, + 504, + 220.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 226, + 505, + 267 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 225, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 225, + 505, + 238 + ], + "score": 1.0, + "content": "Figure B.3: a) Examples from the CelebA brightness dataset. The first three images from the left have", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 235, + 505, + 248 + ], + "spans": [ + { + "bbox": [ + 107, + 237, + 134, + 246 + ], + "score": 0.87, + "content": "y \\equiv n o", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 235, + 284, + 248 + ], + "score": 1.0, + "content": "glasses; the remaining three images have", + "type": "text" + }, + { + "bbox": [ + 284, + 236, + 328, + 246 + ], + "score": 0.73, + "content": "y \\equiv g l a s s e s", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 235, + 505, + 248 + ], + "score": 1.0, + "content": ". Connected images are counterfactual examples.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 245, + 506, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 375, + 257 + ], + "score": 1.0, + "content": "b) Misclassified examples from the test sets. c) Misclassification rates for", + "type": "text" + }, + { + "bbox": [ + 375, + 246, + 405, + 256 + ], + "score": 0.92, + "content": "\\beta = 2 0", + "type": "inline_equation" + }, + { + "bbox": [ + 406, + 245, + 421, + 257 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 421, + 246, + 459, + 255 + ], + "score": 0.89, + "content": "c = 2 0 0 0", + "type": "inline_equation" + }, + { + "bbox": [ + 459, + 245, + 506, + 257 + ], + "score": 1.0, + "content": ". Results for", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 255, + 463, + 267 + ], + "spans": [ + { + "bbox": [ + 106, + 255, + 225, + 267 + ], + "score": 1.0, + "content": "different counterfactual settings,", + "type": "text" + }, + { + "bbox": [ + 225, + 256, + 283, + 267 + ], + "score": 0.93, + "content": "\\beta \\in \\{ 5 , 1 0 , 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 284, + 255, + 299, + 267 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 300, + 256, + 361, + 267 + ], + "score": 0.92, + "content": "c \\in \\{ 2 0 0 , 5 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 362, + 255, + 463, + 267 + ], + "score": 1.0, + "content": "can be found in Figure B.5.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 289, + 505, + 367 + ], + "lines": [], + "index": 10, + "bbox_fs": [ + 105, + 290, + 505, + 369 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 108, + 380, + 304, + 392 + ], + "lines": [ + { + "bbox": [ + 105, + 380, + 306, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 306, + 393 + ], + "score": 1.0, + "content": "B.2.1 COUNTERFACTUAL SETTINGS 2 AND 3", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 400, + 505, + 456 + ], + "lines": [ + { + "bbox": [ + 106, + 400, + 504, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 400, + 504, + 412 + ], + "score": 1.0, + "content": "Above we used the same image to create a counterfactual observation by sampling a different value", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 411, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 505, + 424 + ], + "score": 1.0, + "content": "for the brightness intervention. A plausible alternative is to use a different image of the same person", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 422, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 422, + 279, + 436 + ], + "score": 1.0, + "content": "as counterfactual. We call this “CF setting", + "type": "text" + }, + { + "bbox": [ + 279, + 423, + 289, + 433 + ], + "score": 0.39, + "content": "2 ^ { \\circ }", + "type": "inline_equation" + }, + { + "bbox": [ + 290, + 422, + 505, + 436 + ], + "score": 1.0, + "content": ". For comparison, we also evaluate using an image of", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 432, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 355, + 447 + ], + "score": 1.0, + "content": "a different person as counterfactual as a baseline (“CF setting", + "type": "text" + }, + { + "bbox": [ + 356, + 434, + 367, + 444 + ], + "score": 0.37, + "content": "3 ^ { \\circ }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 432, + 505, + 447 + ], + "score": 1.0, + "content": "). Examples from the training sets", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 444, + 318, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 318, + 457 + ], + "score": 1.0, + "content": "using CF setting 2 and 3 can be found in Figure B.4.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 400, + 505, + 457 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 461, + 505, + 528 + ], + "lines": [ + { + "bbox": [ + 105, + 460, + 505, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 263, + 474 + ], + "score": 1.0, + "content": "Results for all counterfactual settings,", + "type": "text" + }, + { + "bbox": [ + 263, + 461, + 329, + 474 + ], + "score": 0.93, + "content": "\\beta \\in \\{ 5 , 1 0 , 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 329, + 460, + 348, + 474 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 348, + 461, + 417, + 474 + ], + "score": 0.92, + "content": "c \\in \\{ 2 0 0 , 5 0 0 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 417, + 460, + 505, + 474 + ], + "score": 1.0, + "content": "can be found in Fig-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 505, + 484 + ], + "score": 1.0, + "content": "ure B.5. We see that using counterfactual setting 1 works best since we could explicitly control", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 482, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 146, + 497 + ], + "score": 1.0, + "content": "that only", + "type": "text" + }, + { + "bbox": [ + 146, + 483, + 177, + 494 + ], + "score": 0.64, + "content": "X ^ { \\perp } \\equiv", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 482, + 506, + 497 + ], + "score": 1.0, + "content": "brightness varies between counterfactual examples. In counterfactual setting 2,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 493, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 506, + 507 + ], + "score": 1.0, + "content": "different images of the same person can vary in many factors, making it more challenging to isolate", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "brightness as the factor to be invariant against. Lastly, we see that even grouping images of different", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 516, + 353, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 353, + 530 + ], + "score": 1.0, + "content": "persons can still help predictive performance to some degree.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 460, + 506, + 530 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 546, + 495, + 573 + ], + "lines": [ + { + "bbox": [ + 105, + 545, + 497, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 497, + 560 + ], + "score": 1.0, + "content": "C EXPERIMENTAL DETAILS AND ADDITIONAL RESULTS FOR EXPERIMENTS", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 126, + 559, + 267, + 574 + ], + "spans": [ + { + "bbox": [ + 126, + 559, + 267, + 574 + ], + "score": 1.0, + "content": "INTRODUCED IN §2 AND §5", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 26.5 + }, + { + "type": "title", + "bbox": [ + 108, + 585, + 298, + 596 + ], + "lines": [ + { + "bbox": [ + 106, + 585, + 298, + 598 + ], + "spans": [ + { + "bbox": [ + 106, + 585, + 290, + 598 + ], + "score": 1.0, + "content": "C.1 CHOOSING THE TUNING PARAMETER", + "type": "text" + }, + { + "bbox": [ + 291, + 586, + 298, + 595 + ], + "score": 0.46, + "content": "\\lambda", + "type": "inline_equation" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 606, + 505, + 651 + ], + "lines": [ + { + "bbox": [ + 105, + 606, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 375, + 619 + ], + "score": 1.0, + "content": "An open question is how to set the value of the tuning parameter", + "type": "text" + }, + { + "bbox": [ + 375, + 609, + 382, + 617 + ], + "score": 0.75, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 606, + 486, + 619 + ], + "score": 1.0, + "content": "in Eq. (4) or the penalty", + "type": "text" + }, + { + "bbox": [ + 486, + 607, + 493, + 617 + ], + "score": 0.78, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 493, + 606, + 505, + 619 + ], + "score": 1.0, + "content": "in", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 618, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 505, + 630 + ], + "score": 1.0, + "content": "the Lagrangian form. Figure C.6 shows the misclassification rates of CORE on the subsampled", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 343, + 642 + ], + "score": 1.0, + "content": "and augmented AwA2 dataset as a function of the penalty", + "type": "text" + }, + { + "bbox": [ + 344, + 629, + 351, + 639 + ], + "score": 0.72, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 628, + 505, + 642 + ], + "score": 1.0, + "content": ". We see that performance is not very", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 640, + 218, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 207, + 651 + ], + "score": 1.0, + "content": "sensitive to the choice of", + "type": "text" + }, + { + "bbox": [ + 208, + 640, + 215, + 650 + ], + "score": 0.75, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 640, + 218, + 651 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 606, + 505, + 651 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 666, + 471, + 678 + ], + "lines": [ + { + "bbox": [ + 115, + 666, + 462, + 678 + ], + "spans": [ + { + "bbox": [ + 115, + 666, + 462, + 678 + ], + "score": 1.0, + "content": ".2 GROUPING PHOTOS OF THE SAME PERSON: BETTER PREDICTIVE PERFORMAN", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 108, + 687, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 359, + 700 + ], + "score": 1.0, + "content": "Here, we show further results for the experiment introduced in", + "type": "text" + }, + { + "bbox": [ + 359, + 688, + 377, + 699 + ], + "score": 0.82, + "content": "\\ S 2 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 687, + 505, + 700 + ], + "score": 1.0, + "content": ". We vary the number of identi-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 699, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 252, + 711 + ], + "score": 1.0, + "content": "ties included in the training data set", + "type": "text" + }, + { + "bbox": [ + 253, + 699, + 355, + 711 + ], + "score": 0.9, + "content": "n \\in \\{ 1 0 , 2 0 , 4 0 , 8 0 , 1 6 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 356, + 699, + 494, + 711 + ], + "score": 1.0, + "content": ". This results in total sample sizes", + "type": "text" + }, + { + "bbox": [ + 494, + 701, + 504, + 709 + ], + "score": 0.5, + "content": "m", + "type": "inline_equation" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 195, + 722 + ], + "score": 1.0, + "content": "ranging from 321 for", + "type": "text" + }, + { + "bbox": [ + 195, + 710, + 227, + 720 + ], + "score": 0.9, + "content": "n = 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 710, + 277, + 722 + ], + "score": 1.0, + "content": "to 4386 for", + "type": "text" + }, + { + "bbox": [ + 277, + 711, + 315, + 720 + ], + "score": 0.88, + "content": "n = 1 6 0", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 710, + 505, + 722 + ], + "score": 1.0, + "content": ", implying that the average number of counter-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 371, + 733 + ], + "score": 1.0, + "content": "factual observations per person varies between 27 and 32. Figure", + "type": "text" + }, + { + "bbox": [ + 372, + 721, + 393, + 731 + ], + "score": 0.28, + "content": "{ \\mathrm { C . 7 b } }", + "type": "inline_equation" + }, + { + "bbox": [ + 393, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "shows the misclassification", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 455, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 468 + ], + "score": 1.0, + "content": "rates for the test set which consists of 5000 examples. We see that CORE helps predictive perfor-", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 412, + 479 + ], + "score": 1.0, + "content": "mance compared to the estimator which just pools all images, notably when", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 412, + 469, + 419, + 477 + ], + "score": 0.72, + "content": "n", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 420, + 467, + 505, + 479 + ], + "score": 1.0, + "content": "is very small. It thus", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 478, + 504, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 496, + 491 + ], + "score": 1.0, + "content": "successfully mitigates the effect of potential confounders arising due to small sample sizes. As", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 497, + 480, + 504, + 488 + ], + "score": 0.6, + "content": "n", + "type": "inline_equation", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 123, + 502 + ], + "score": 1.0, + "content": "and", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 123, + 490, + 133, + 499 + ], + "score": 0.74, + "content": "m", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 134, + 488, + 505, + 502 + ], + "score": 1.0, + "content": "increase the performance of CORE and the pooled estimator become comparable—the larger", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 498, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 104, + 498, + 505, + 514 + ], + "score": 1.0, + "content": "sample sizes ensure that fewer confounding factors are present in the training data and exploited by", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 510, + 192, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 192, + 523 + ], + "score": 1.0, + "content": "the pooled estimator.", + "type": "text", + "cross_page": true + } + ], + "index": 13 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 687, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 110, + 87, + 501, + 313 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 110, + 87, + 501, + 313 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 110, + 87, + 501, + 313 + ], + "spans": [ + { + "bbox": [ + 110, + 87, + 501, + 313 + ], + "score": 0.975, + "type": "image", + "image_path": "6fb23cf7597ce0bfd497baca22426a641baef6f9bc618d2b2178e4f022941491.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 110, + 87, + 501, + 162.33333333333331 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 110, + 162.33333333333331, + 501, + 237.66666666666663 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 110, + 237.66666666666663, + 501, + 312.99999999999994 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 321, + 506, + 371 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 321, + 505, + 333 + ], + "spans": [ + { + "bbox": [ + 106, + 321, + 443, + 333 + ], + "score": 1.0, + "content": "Figure B.4: Examples from the CelebA brightness datasets, counterfactual settings 1–3 with", + "type": "text" + }, + { + "bbox": [ + 443, + 321, + 501, + 332 + ], + "score": 0.91, + "content": "\\beta \\in \\{ 5 , 1 0 , 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 321, + 505, + 333 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 330, + 505, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 300, + 343 + ], + "score": 1.0, + "content": "In all rows, the first three images from the left have", + "type": "text" + }, + { + "bbox": [ + 301, + 333, + 331, + 342 + ], + "score": 0.8, + "content": "y \\equiv n o", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 330, + 486, + 343 + ], + "score": 1.0, + "content": "glasses; the remaining three images have", + "type": "text" + }, + { + "bbox": [ + 487, + 333, + 505, + 342 + ], + "score": 0.86, + "content": "y \\equiv", + "type": "inline_equation" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 342, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 106, + 342, + 505, + 353 + ], + "score": 1.0, + "content": "glasses. Connected images are counterfactual examples. In panels (a)–(c), row 1 shows examples from the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 351, + 505, + 362 + ], + "spans": [ + { + "bbox": [ + 106, + 351, + 505, + 362 + ], + "score": 1.0, + "content": "training set, rows 2–4 contain examples from test sets 2–4, respectively. Panels (d)–(i) show examples from the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 361, + 193, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 193, + 374 + ], + "score": 1.0, + "content": "respective training sets.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 106, + 455, + 505, + 522 + ], + "lines": [ + { + "bbox": [ + 105, + 455, + 505, + 468 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 468 + ], + "score": 1.0, + "content": "rates for the test set which consists of 5000 examples. We see that CORE helps predictive perfor-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 412, + 479 + ], + "score": 1.0, + "content": "mance compared to the estimator which just pools all images, notably when", + "type": "text" + }, + { + "bbox": [ + 412, + 469, + 419, + 477 + ], + "score": 0.72, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 420, + 467, + 505, + 479 + ], + "score": 1.0, + "content": "is very small. It thus", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 478, + 504, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 496, + 491 + ], + "score": 1.0, + "content": "successfully mitigates the effect of potential confounders arising due to small sample sizes. As", + "type": "text" + }, + { + "bbox": [ + 497, + 480, + 504, + 488 + ], + "score": 0.6, + "content": "n", + "type": "inline_equation" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 488, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 123, + 502 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 123, + 490, + 133, + 499 + ], + "score": 0.74, + "content": "m", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 488, + 505, + 502 + ], + "score": 1.0, + "content": "increase the performance of CORE and the pooled estimator become comparable—the larger", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 498, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 104, + 498, + 505, + 514 + ], + "score": 1.0, + "content": "sample sizes ensure that fewer confounding factors are present in the training data and exploited by", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 510, + 192, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 510, + 192, + 523 + ], + "score": 1.0, + "content": "the pooled estimator.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 10.5 + } + ], + "page_idx": 21, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 27, + 308, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 309, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 309, + 38 + ], + "score": 1.0, + "content": "Under review as a conference paper at ICLR 2018", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "22", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 606, + 446, + 617 + ], + "lines": [ + { + "bbox": [ + 105, + 605, + 448, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 448, + 619 + ], + "score": 1.0, + "content": "C.3 GROUPING AUGMENTED IMAGES BY ORIGINAL: MORE SAMPLE EFFICIENT", + "type": "text" + } + ] + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 654, + 505, + 732 + ], + "lines": [] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 110, + 87, + 501, + 313 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 110, + 87, + 501, + 313 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 110, + 87, + 501, + 313 + ], + "spans": [ + { + "bbox": [ + 110, + 87, + 501, + 313 + ], + "score": 0.975, + "type": "image", + "image_path": "6fb23cf7597ce0bfd497baca22426a641baef6f9bc618d2b2178e4f022941491.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 110, + 87, + 501, + 162.33333333333331 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 110, + 162.33333333333331, + 501, + 237.66666666666663 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 110, + 237.66666666666663, + 501, + 312.99999999999994 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 321, + 506, + 371 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 321, + 505, + 333 + ], + "spans": [ + { + "bbox": [ + 106, + 321, + 443, + 333 + ], + "score": 1.0, + "content": "Figure B.4: Examples from the CelebA brightness datasets, counterfactual settings 1–3 with", + "type": "text" + }, + { + "bbox": [ + 443, + 321, + 501, + 332 + ], + "score": 0.91, + "content": "\\beta \\in \\{ 5 , 1 0 , 2 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 321, + 505, + 333 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 330, + 505, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 300, + 343 + ], + "score": 1.0, + "content": "In all rows, the first three images from the left have", + "type": "text" + }, + { + "bbox": [ + 301, + 333, + 331, + 342 + ], + "score": 0.8, + "content": "y \\equiv n o", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 330, + 486, + 343 + ], + "score": 1.0, + "content": "glasses; the remaining three images have", + "type": "text" + }, + { + "bbox": [ + 487, + 333, + 505, + 342 + ], + "score": 0.86, + "content": "y \\equiv", + "type": "inline_equation" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 342, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 106, + 342, + 505, + 353 + ], + "score": 1.0, + "content": "glasses. 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Figure C.11 shows examples", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "from the respective training and test sets and Figure C.12 shows the corresponding misclassification", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 710, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 721 + ], + "score": 1.0, + "content": "rates. Again, we observe that counterfactual setting 1 works best while there are only small differ-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 721, + 506, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 506, + 734 + ], + "score": 1.0, + "content": "ences in predictive performance between counterfactual settings 2 and 3. 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In", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 227, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 285, + 239 + ], + "score": 1.0, + "content": "each row, the first three images from the left have", + "type": "text" + }, + { + "bbox": [ + 286, + 227, + 322, + 238 + ], + "score": 0.67, + "content": "y \\equiv c h i l d", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 227, + 444, + 239 + ], + "score": 1.0, + "content": "; the remaining three images have", + "type": "text" + }, + { + "bbox": [ + 444, + 227, + 481, + 238 + ], + "score": 0.64, + "content": "y \\equiv a d u l t", + "type": "inline_equation" + }, + { + "bbox": [ + 481, + 227, + 505, + 239 + ], + "score": 1.0, + "content": ". 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Figure C.10b shows results", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 493, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 329, + 506 + ], + "score": 1.0, + "content": "for different numbers of counterfactual examples. For", + "type": "text" + }, + { + "bbox": [ + 329, + 494, + 361, + 504 + ], + "score": 0.89, + "content": "c = 2 0", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 493, + 505, + 506 + ], + "score": 1.0, + "content": "the misclassification rate of CORE", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 504, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 247, + 516 + ], + "score": 1.0, + "content": "estimator has a large variance. 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The pooled estimator fails to achieve", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 537, + 506, + 550 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 506, + 550 + ], + "score": 1.0, + "content": "good predictive performance on test sets 2 and 3 as it seems to use “movement” as a predictor for", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 547, + 136, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 136, + 562 + ], + "score": 1.0, + "content": "“age”.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 23, + "bbox_fs": [ + 105, + 482, + 506, + 562 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 573, + 384, + 585 + ], + "lines": [ + { + "bbox": [ + 106, + 573, + 385, + 586 + ], + "spans": [ + { + "bbox": [ + 106, + 573, + 385, + 586 + ], + "score": 1.0, + "content": "C.5 EYEGLASSES DETECTION: IMAGE QUALITY INTERVENTION", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 594, + 505, + 682 + ], + "lines": [ + { + "bbox": [ + 105, + 593, + 505, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 357, + 607 + ], + "score": 1.0, + "content": "Here, we show further results for the experiment introduced in", + "type": "text" + }, + { + "bbox": [ + 357, + 594, + 375, + 605 + ], + "score": 0.68, + "content": "\\ S 5 . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 593, + 505, + 607 + ], + "score": 1.0, + "content": ". Specifically, we consider inter-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 432, + 618 + ], + "score": 1.0, + "content": "ventions of different strengths by varying the mean of the quality intervention in", + "type": "text" + }, + { + "bbox": [ + 433, + 605, + 501, + 617 + ], + "score": 0.91, + "content": "\\mu \\in \\{ 3 0 , 4 0 , 5 0 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 605, + 505, + 618 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 616, + 506, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 132, + 629 + ], + "score": 1.0, + "content": "As in", + "type": "text" + }, + { + "bbox": [ + 132, + 616, + 152, + 628 + ], + "score": 0.87, + "content": "\\mathrm { \\ S B } . 2", + "type": "inline_equation" + }, + { + "bbox": [ + 152, + 616, + 506, + 629 + ], + "score": 1.0, + "content": ", we use ImageMagick, this time to modify the image quality. 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Figure C.11 shows examples", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "from the respective training and test sets and Figure C.12 shows the corresponding misclassification", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 710, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 721 + ], + "score": 1.0, + "content": "rates. Again, we observe that counterfactual setting 1 works best while there are only small differ-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 721, + 506, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 506, + 734 + ], + "score": 1.0, + "content": "ences in predictive performance between counterfactual settings 2 and 3. 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For small", + "type": "text" + }, + { + "bbox": [ + 480, + 617, + 487, + 625 + ], + "score": 0.65, + "content": "c", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 614, + 505, + 628 + ], + "score": 1.0, + "content": "this", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 625, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 505, + 640 + ], + "score": 1.0, + "content": "implies that not all mini batches contain counterfactual observations, making the optimization more", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 635, + 159, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 159, + 651 + ], + "score": 1.0, + "content": "challenging.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35, + "bbox_fs": [ + 105, + 592, + 505, + 651 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 122, + 297, + 486, + 487 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 122, + 297, + 486, + 487 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 122, + 297, + 486, + 487 + ], + "spans": [ + { + "bbox": [ + 122, + 297, + 486, + 487 + ], + "score": 0.984, + "html": "
DatasetOptimizerArchitecture
MNISTAdamInput CNN28×28×1 Conv5×5×16,5×5×32
StickmenAdamInput CNN(same padding,strides= 2,ReLu activation), fully connected, softmax layer 64×64×1 Conv5×5×16,5×5×32,5×5×64,5×5×128
CelebA (all experimentsAdamInput CNN(same padding,strides = 2, leaky ReLu activation), fully connected, softmax layer 64×48×3 Conv5×5×16,5×5×32,5×5×64,5×5×128
using CelebA) AwA2AdamInput(same padding,strides = 2,leaky ReLu activation), fully connected, softmax layer
CNN32 ×32×3 Conv5×5×16,5×5×32,5×5×64,5×5×128 (same padding,strides = 2,leaky ReLu activation), fully connected, softmax layer
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DatasetOptimizerArchitecture
MNISTAdamInput CNN28×28×1 Conv5×5×16,5×5×32
StickmenAdamInput CNN(same padding,strides= 2,ReLu activation), fully connected, softmax layer 64×64×1 Conv5×5×16,5×5×32,5×5×64,5×5×128
CelebA (all experimentsAdamInput CNN(same padding,strides = 2, leaky ReLu activation), fully connected, softmax layer 64×48×3 Conv5×5×16,5×5×32,5×5×64,5×5×128
using CelebA) AwA2AdamInput(same padding,strides = 2,leaky ReLu activation), fully connected, softmax layer
CNN32 ×32×3 Conv5×5×16,5×5×32,5×5×64,5×5×128 (same padding,strides = 2,leaky ReLu activation), fully connected, softmax layer
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