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Assuming a view of the Random Forest as a special case of a nested ensemble of interchangeable modules, we construct a generalisation space allowing one to easily develop novel methods based on this algorithm. We discuss the role and required properties of modules at each level, especially in context of some already proposed RF generalisations. | Generalised Random Forest Space Overview | 2,800 |
In [1], a clustering algorithm was given to find the centers of clusters quickly. However, the accuracy of this algorithm heavily depend on the threshold value of d-c. Furthermore, [1] has not provided any efficient way to select the threshold value of d-c, that is, one can have to estimate the value of d_c depend on one's subjective experience. In this paper, based on the data field [2], we propose a new way to automatically extract the threshold value of d_c from the original data set by using the potential entropy of data field. For any data set to be clustered, the most reasonable value of d_c can be objectively calculated from the data set by using our proposed method. The same experiments in [1] are redone with our proposed method on the same experimental data set used in [1], the results of which shows that the problem to calculate the threshold value of d_c in [1] has been solved by using our method. | Comment on "Clustering by fast search and find of density peaks" | 2,801 |
In this paper we investigate the usage of regularized correntropy framework for learning of classifiers from noisy labels. The class label predictors learned by minimizing transitional loss functions are sensitive to the noisy and outlying labels of training samples, because the transitional loss functions are equally applied to all the samples. To solve this problem, we propose to learn the class label predictors by maximizing the correntropy between the predicted labels and the true labels of the training samples, under the regularized Maximum Correntropy Criteria (MCC) framework. Moreover, we regularize the predictor parameter to control the complexity of the predictor. The learning problem is formulated by an objective function considering the parameter regularization and MCC simultaneously. By optimizing the objective function alternately, we develop a novel predictor learning algorithm. The experiments on two chal- lenging pattern classification tasks show that it significantly outperforms the machines with transitional loss functions. | Regularized maximum correntropy machine | 2,802 |
Most of the existing classification methods are aimed at minimization of empirical risk (through some simple point-based error measured with loss function) with added regularization. We propose to approach this problem in a more information theoretic way by investigating applicability of entropy measures as a classification model objective function. We focus on quadratic Renyi's entropy and connected Cauchy-Schwarz Divergence which leads to the construction of Extreme Entropy Machines (EEM). The main contribution of this paper is proposing a model based on the information theoretic concepts which on the one hand shows new, entropic perspective on known linear classifiers and on the other leads to a construction of very robust method competetitive with the state of the art non-information theoretic ones (including Support Vector Machines and Extreme Learning Machines). Evaluation on numerous problems spanning from small, simple ones from UCI repository to the large (hundreads of thousands of samples) extremely unbalanced (up to 100:1 classes' ratios) datasets shows wide applicability of the EEM in real life problems and that it scales well. | Extreme Entropy Machines: Robust information theoretic classification | 2,803 |
Semi-supervised clustering is an very important topic in machine learning and computer vision. The key challenge of this problem is how to learn a metric, such that the instances sharing the same label are more likely close to each other on the embedded space. However, little attention has been paid to learn better representations when the data lie on non-linear manifold. Fortunately, deep learning has led to great success on feature learning recently. Inspired by the advances of deep learning, we propose a deep transductive semi-supervised maximum margin clustering approach. More specifically, given pairwise constraints, we exploit both labeled and unlabeled data to learn a non-linear mapping under maximum margin framework for clustering analysis. Thus, our model unifies transductive learning, feature learning and maximum margin techniques in the semi-supervised clustering framework. We pretrain the deep network structure with restricted Boltzmann machines (RBMs) layer by layer greedily, and optimize our objective function with gradient descent. By checking the most violated constraints, our approach updates the model parameters through error backpropagation, in which deep features are learned automatically. The experimental results shows that our model is significantly better than the state of the art on semi-supervised clustering. | Deep Transductive Semi-supervised Maximum Margin Clustering | 2,804 |
In many applications data is naturally presented in terms of orderings of some basic elements or symbols. Reasoning about such data requires a notion of similarity capable of handling sequences of different lengths. In this paper we describe a family of Mercer kernel functions for such sequentially structured data. The family is characterized by a decomposable structure in terms of symbol-level and structure-level similarities, representing a specific combination of kernels which allows for efficient computation. We provide an experimental evaluation on sequential classification tasks comparing kernels from our family of kernels to a state of the art sequence kernel called the Global Alignment kernel which has been shown to outperform Dynamic Time Warping | On a Family of Decomposable Kernels on Sequences | 2,805 |
Support vector machines (SVM) can classify data sets along highly non-linear decision boundaries because of the kernel-trick. This expressiveness comes at a price: During test-time, the SVM classifier needs to compute the kernel inner-product between a test sample and all support vectors. With large training data sets, the time required for this computation can be substantial. In this paper, we introduce a post-processing algorithm, which compresses the learned SVM model by reducing and optimizing support vectors. We evaluate our algorithm on several medium-scaled real-world data sets, demonstrating that it maintains high test accuracy while reducing the test-time evaluation cost by several orders of magnitude---in some cases from hours to seconds. It is fair to say that most of the work in this paper was previously been invented by Burges and Sch\"olkopf almost 20 years ago. For most of the time during which we conducted this research, we were unaware of this prior work. However, in the past two decades, computing power has increased drastically, and we can therefore provide empirical insights that were not possible in their original paper. | Compressed Support Vector Machines | 2,806 |
Coronary heart disease (CHD) caused by hardening of artery walls due to cholesterol known as atherosclerosis is responsible for large number of deaths world-wide. The disease progression is slow, asymptomatic and may lead to sudden cardiac arrest, stroke or myocardial infraction. Presently, imaging techniques are being employed to understand the molecular and metabolic activity of atherosclerotic plaques to estimate the risk. Though imaging methods are able to provide some information on plaque metabolism they lack the required resolution and sensitivity for detection. In this paper we consider the clinical observations and habits of individuals for predicting the risk factors of CHD. The identification of risk factors helps in stratifying patients for further intensive tests such as nuclear imaging or coronary angiography. We present a novel approach for predicting the risk factors of atherosclerosis with an in-built imputation algorithm and particle swarm optimization (PSO). We compare the performance of our methodology with other machine learning techniques on STULONG dataset which is based on longitudinal study of middle aged individuals lasting for twenty years. Our methodology powered by PSO search has identified physical inactivity as one of the risk factor for the onset of atherosclerosis in addition to other already known factors. The decision rules extracted by our methodology are able to predict the risk factors with an accuracy of $99.73%$ which is higher than the accuracies obtained by application of the state-of-the-art machine learning techniques presently being employed in the identification of atherosclerosis risk studies. | Novel Approaches for Predicting Risk Factors of Atherosclerosis | 2,807 |
Applications involving dictionary learning, non-negative matrix factorization, subspace clustering, and parallel factor tensor decomposition tasks motivate well algorithms for per-block-convex and non-smooth optimization problems. By leveraging the stochastic approximation paradigm and first-order acceleration schemes, this paper develops an online and modular learning algorithm for a large class of non-convex data models, where convexity is manifested only per-block of variables whenever the rest of them are held fixed. The advocated algorithm incurs computational complexity that scales linearly with the number of unknowns. Under minimal assumptions on the cost functions of the composite optimization task, without bounding constraints on the optimization variables, or any explicit information on bounds of Lipschitz coefficients, the expected cost evaluated online at the resultant iterates is provably convergent with quadratic rate to an accumulation point of the (per-block) minima, while subgradients of the expected cost asymptotically vanish in the mean-squared sense. The merits of the general approach are demonstrated in two online learning setups: (i) Robust linear regression using a sparsity-cognizant total least-squares criterion; and (ii) semi-supervised dictionary learning for network-wide link load tracking and imputation with missing entries. Numerical tests on synthetic and real data highlight the potential of the proposed framework for streaming data analytics by demonstrating superior performance over block coordinate descent, and reduced complexity relative to the popular alternating-direction method of multipliers. | Per-Block-Convex Data Modeling by Accelerated Stochastic Approximation | 2,808 |
This study presents a divide-and-conquer (DC) approach based on feature space decomposition for classification. When large-scale datasets are present, typical approaches usually employed truncated kernel methods on the feature space or DC approaches on the sample space. However, this did not guarantee separability between classes, owing to overfitting. To overcome such problems, this work proposes a novel DC approach on feature spaces consisting of three steps. Firstly, we divide the feature space into several subspaces using the decomposition method proposed in this paper. Subsequently, these feature subspaces are sent into individual local classifiers for training. Finally, the outcomes of local classifiers are fused together to generate the final classification results. Experiments on large-scale datasets are carried out for performance evaluation. The results show that the error rates of the proposed DC method decreased comparing with the state-of-the-art fast SVM solvers, e.g., reducing error rates by 10.53% and 7.53% on RCV1 and covtype datasets respectively. | Efficient Divide-And-Conquer Classification Based on Feature-Space
Decomposition | 2,809 |
Vector Symbolic Architectures (VSAs) are high-dimensional vector representations of objects (eg., words, image parts), relations (eg., sentence structures), and sequences for use with machine learning algorithms. They consist of a vector addition operator for representing a collection of unordered objects, a Binding operator for associating groups of objects, and a methodology for encoding complex structures. We first develop Constraints that machine learning imposes upon VSAs: for example, similar structures must be represented by similar vectors. The constraints suggest that current VSAs should represent phrases ("The smart Brazilian girl") by binding sums of terms, in addition to simply binding the terms directly. We show that matrix multiplication can be used as the binding operator for a VSA, and that matrix elements can be chosen at random. A consequence for living systems is that binding is mathematically possible without the need to specify, in advance, precise neuron-to-neuron connection properties for large numbers of synapses. A VSA that incorporates these ideas, MBAT (Matrix Binding of Additive Terms), is described that satisfies all Constraints. With respect to machine learning, for some types of problems appropriate VSA representations permit us to prove learnability, rather than relying on simulations. We also propose dividing machine (and neural) learning and representation into three Stages, with differing roles for learning in each stage. For neural modeling, we give "representational reasons" for nervous systems to have many recurrent connections, as well as for the importance of phrases in language processing. Sizing simulations and analyses suggest that VSAs in general, and MBAT in particular, are ready for real-world applications. | Representing Objects, Relations, and Sequences | 2,810 |
We propose a batchwise monotone algorithm for dictionary learning. Unlike the state-of-the-art dictionary learning algorithms which impose sparsity constraints on a sample-by-sample basis, we instead treat the samples as a batch, and impose the sparsity constraint on the whole. The benefit of batchwise optimization is that the non-zeros can be better allocated across the samples, leading to a better approximation of the whole. To accomplish this, we propose procedures to switch non-zeros in both rows and columns in the support of the coefficient matrix to reduce the reconstruction error. We prove in the proposed support switching procedure the objective of the algorithm, i.e., the reconstruction error, decreases monotonically and converges. Furthermore, we introduce a block orthogonal matching pursuit algorithm that also operates on sample batches to provide a warm start. Experiments on both natural image patches and UCI data sets show that the proposed algorithm produces a better approximation with the same sparsity levels compared to the state-of-the-art algorithms. | A Batchwise Monotone Algorithm for Dictionary Learning | 2,811 |
We often encounter situations in which an experimenter wants to find, by sequential experimentation, $x_{max} = \arg\max_{x} f(x)$, where $f(x)$ is a (possibly unknown) function of a well controllable variable $x$. Taking inspiration from physics and engineering, we have designed a new method to address this problem. In this paper, we first introduce the method in continuous time, and then present two algorithms for use in sequential experiments. Through a series of simulation studies, we show that the method is effective for finding maxima of unknown functions by experimentation, even when the maximum of the functions drifts or when the signal to noise ratio is low. | Lock in Feedback in Sequential Experiments | 2,812 |
In various applications involving hidden Markov models (HMMs), some of the hidden states are aliased, having identical output distributions. The minimality, identifiability and learnability of such aliased HMMs have been long standing problems, with only partial solutions provided thus far. In this paper we focus on parametric-output HMMs, whose output distributions come from a parametric family, and that have exactly two aliased states. For this class, we present a complete characterization of their minimality and identifiability. Furthermore, for a large family of parametric output distributions, we derive computationally efficient and statistically consistent algorithms to detect the presence of aliasing and learn the aliased HMM transition and emission parameters. We illustrate our theoretical analysis by several simulations. | Learning Parametric-Output HMMs with Two Aliased States | 2,813 |
We propose a new algorithm for minimizing regularized empirical loss: Stochastic Dual Newton Ascent (SDNA). Our method is dual in nature: in each iteration we update a random subset of the dual variables. However, unlike existing methods such as stochastic dual coordinate ascent, SDNA is capable of utilizing all curvature information contained in the examples, which leads to striking improvements in both theory and practice - sometimes by orders of magnitude. In the special case when an L2-regularizer is used in the primal, the dual problem is a concave quadratic maximization problem plus a separable term. In this regime, SDNA in each step solves a proximal subproblem involving a random principal submatrix of the Hessian of the quadratic function; whence the name of the method. If, in addition, the loss functions are quadratic, our method can be interpreted as a novel variant of the recently introduced Iterative Hessian Sketch. | SDNA: Stochastic Dual Newton Ascent for Empirical Risk Minimization | 2,814 |
The minimization of the logistic loss is a popular approach to batch supervised learning. Our paper starts from the surprising observation that, when fitting linear (or kernelized) classifiers, the minimization of the logistic loss is \textit{equivalent} to the minimization of an exponential \textit{rado}-loss computed (i) over transformed data that we call Rademacher observations (rados), and (ii) over the \textit{same} classifier as the one of the logistic loss. Thus, a classifier learnt from rados can be \textit{directly} used to classify \textit{observations}. We provide a learning algorithm over rados with boosting-compliant convergence rates on the \textit{logistic loss} (computed over examples). Experiments on domains with up to millions of examples, backed up by theoretical arguments, display that learning over a small set of random rados can challenge the state of the art that learns over the \textit{complete} set of examples. We show that rados comply with various privacy requirements that make them good candidates for machine learning in a privacy framework. We give several algebraic, geometric and computational hardness results on reconstructing examples from rados. We also show how it is possible to craft, and efficiently learn from, rados in a differential privacy framework. Tests reveal that learning from differentially private rados can compete with learning from random rados, and hence with batch learning from examples, achieving non-trivial privacy vs accuracy tradeoffs. | Rademacher Observations, Private Data, and Boosting | 2,815 |
We present a mathematical construction for the restricted Boltzmann machine (RBM) that doesn't require specifying the number of hidden units. In fact, the hidden layer size is adaptive and can grow during training. This is obtained by first extending the RBM to be sensitive to the ordering of its hidden units. Then, thanks to a carefully chosen definition of the energy function, we show that the limit of infinitely many hidden units is well defined. As with RBM, approximate maximum likelihood training can be performed, resulting in an algorithm that naturally and adaptively adds trained hidden units during learning. We empirically study the behaviour of this infinite RBM, showing that its performance is competitive to that of the RBM, while not requiring the tuning of a hidden layer size. | An Infinite Restricted Boltzmann Machine | 2,816 |
We present a novel adaptive random subspace learning algorithm (RSSL) for prediction purpose. This new framework is flexible where it can be adapted with any learning technique. In this paper, we tested the algorithm for regression and classification problems. In addition, we provide a variety of weighting schemes to increase the robustness of the developed algorithm. These different wighting flavors were evaluated on simulated as well as on real-world data sets considering the cases where the ratio between features (attributes) and instances (samples) is large and vice versa. The framework of the new algorithm consists of many stages: first, calculate the weights of all features on the data set using the correlation coefficient and F-statistic statistical measurements. Second, randomly draw n samples with replacement from the data set. Third, perform regular bootstrap sampling (bagging). Fourth, draw without replacement the indices of the chosen variables. The decision was taken based on the heuristic subspacing scheme. Fifth, call base learners and build the model. Sixth, use the model for prediction purpose on test set of the data. The results show the advancement of the adaptive RSSL algorithm in most of the cases compared with the synonym (conventional) machine learning algorithms. | Adaptive Random SubSpace Learning (RSSL) Algorithm for Prediction | 2,817 |
We study online boosting, the task of converting any weak online learner into a strong online learner. Based on a novel and natural definition of weak online learnability, we develop two online boosting algorithms. The first algorithm is an online version of boost-by-majority. By proving a matching lower bound, we show that this algorithm is essentially optimal in terms of the number of weak learners and the sample complexity needed to achieve a specified accuracy. This optimal algorithm is not adaptive however. Using tools from online loss minimization, we derive an adaptive online boosting algorithm that is also parameter-free, but not optimal. Both algorithms work with base learners that can handle example importance weights directly, as well as by rejection sampling examples with probability defined by the booster. Results are complemented with an extensive experimental study. | Optimal and Adaptive Algorithms for Online Boosting | 2,818 |
Modeling the dependence between outputs is a fundamental challenge in multilabel classification. In this work we show that a generic regularized nonlinearity mapping independent predictions to joint predictions is sufficient to achieve state-of-the-art performance on a variety of benchmark problems. Crucially, we compute the joint predictions without ever obtaining any independent predictions, while incorporating low-rank and smoothness regularization. We achieve this by leveraging randomized algorithms for matrix decomposition and kernel approximation. Furthermore, our techniques are applicable to the multiclass setting. We apply our method to a variety of multiclass and multilabel data sets, obtaining state-of-the-art results. | Scalable Multilabel Prediction via Randomized Methods | 2,819 |
Recent studies reveal that a deep neural network can learn transferable features which generalize well to novel tasks for domain adaptation. However, as deep features eventually transition from general to specific along the network, the feature transferability drops significantly in higher layers with increasing domain discrepancy. Hence, it is important to formally reduce the dataset bias and enhance the transferability in task-specific layers. In this paper, we propose a new Deep Adaptation Network (DAN) architecture, which generalizes deep convolutional neural network to the domain adaptation scenario. In DAN, hidden representations of all task-specific layers are embedded in a reproducing kernel Hilbert space where the mean embeddings of different domain distributions can be explicitly matched. The domain discrepancy is further reduced using an optimal multi-kernel selection method for mean embedding matching. DAN can learn transferable features with statistical guarantees, and can scale linearly by unbiased estimate of kernel embedding. Extensive empirical evidence shows that the proposed architecture yields state-of-the-art image classification error rates on standard domain adaptation benchmarks. | Learning Transferable Features with Deep Adaptation Networks | 2,820 |
Training Deep Neural Networks is complicated by the fact that the distribution of each layer's inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization. It also acts as a regularizer, in some cases eliminating the need for Dropout. Applied to a state-of-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.9% top-5 validation error (and 4.8% test error), exceeding the accuracy of human raters. | Batch Normalization: Accelerating Deep Network Training by Reducing
Internal Covariate Shift | 2,821 |
Metric learning has been shown to be highly effective to improve the performance of nearest neighbor classification. In this paper, we address the problem of metric learning for Symmetric Positive Definite (SPD) matrices such as covariance matrices, which arise in many real-world applications. Naively using standard Mahalanobis metric learning methods under the Euclidean geometry for SPD matrices is not appropriate, because the difference of SPD matrices can be a non-SPD matrix and thus the obtained solution can be uninterpretable. To cope with this problem, we propose to use a properly parameterized LogEuclidean distance and optimize the metric with respect to kernel-target alignment, which is a supervised criterion for kernel learning. Then the resulting non-trivial optimization problem is solved by utilizing the Riemannian geometry. Finally, we experimentally demonstrate the usefulness of our LogEuclidean metric learning algorithm on real-world classification tasks for EEG signals and texture patches. | Supervised LogEuclidean Metric Learning for Symmetric Positive Definite
Matrices | 2,822 |
Distributed optimization methods for large-scale machine learning suffer from a communication bottleneck. It is difficult to reduce this bottleneck while still efficiently and accurately aggregating partial work from different machines. In this paper, we present a novel generalization of the recent communication-efficient primal-dual framework (CoCoA) for distributed optimization. Our framework, CoCoA+, allows for additive combination of local updates to the global parameters at each iteration, whereas previous schemes with convergence guarantees only allow conservative averaging. We give stronger (primal-dual) convergence rate guarantees for both CoCoA as well as our new variants, and generalize the theory for both methods to cover non-smooth convex loss functions. We provide an extensive experimental comparison that shows the markedly improved performance of CoCoA+ on several real-world distributed datasets, especially when scaling up the number of machines. | Adding vs. Averaging in Distributed Primal-Dual Optimization | 2,823 |
Stochastic alternating direction method of multipliers (ADMM), which visits only one sample or a mini-batch of samples each time, has recently been proved to achieve better performance than batch ADMM. However, most stochastic methods can only achieve a convergence rate $O(1/\sqrt T)$ on general convex problems,where T is the number of iterations. Hence, these methods are not scalable with respect to convergence rate (computation cost). There exists only one stochastic method, called SA-ADMM, which can achieve convergence rate $O(1/T)$ on general convex problems. However, an extra memory is needed for SA-ADMM to store the historic gradients on all samples, and thus it is not scalable with respect to storage cost. In this paper, we propose a novel method, called scalable stochastic ADMM(SCAS-ADMM), for large-scale optimization and learning problems. Without the need to store the historic gradients, SCAS-ADMM can achieve the same convergence rate $O(1/T)$ as the best stochastic method SA-ADMM and batch ADMM on general convex problems. Experiments on graph-guided fused lasso show that SCAS-ADMM can achieve state-of-the-art performance in real applications | Scalable Stochastic Alternating Direction Method of Multipliers | 2,824 |
Bankruptcy is a legal procedure that claims a person or organization as a debtor. It is essential to ascertain the risk of bankruptcy at initial stages to prevent financial losses. In this perspective, different soft computing techniques can be employed to ascertain bankruptcy. This study proposes a bankruptcy prediction system to categorize the companies based on extent of risk. The prediction system acts as a decision support tool for detection of bankruptcy Keywords: Bankruptcy, soft computing, decision support tool | A Predictive System for detection of Bankruptcy using Machine Learning
techniques | 2,825 |
We give a new deterministic algorithm that non-adaptively learns a hidden hypergraph from edge-detecting queries. All previous non-adaptive algorithms either run in exponential time or have non-optimal query complexity. We give the first polynomial time non-adaptive learning algorithm for learning hypergraph that asks almost optimal number of queries. | Non-Adaptive Learning a Hidden Hipergraph | 2,826 |
Neuroscientists have long criticised deep learning algorithms as incompatible with current knowledge of neurobiology. We explore more biologically plausible versions of deep representation learning, focusing here mostly on unsupervised learning but developing a learning mechanism that could account for supervised, unsupervised and reinforcement learning. The starting point is that the basic learning rule believed to govern synaptic weight updates (Spike-Timing-Dependent Plasticity) arises out of a simple update rule that makes a lot of sense from a machine learning point of view and can be interpreted as gradient descent on some objective function so long as the neuronal dynamics push firing rates towards better values of the objective function (be it supervised, unsupervised, or reward-driven). The second main idea is that this corresponds to a form of the variational EM algorithm, i.e., with approximate rather than exact posteriors, implemented by neural dynamics. Another contribution of this paper is that the gradients required for updating the hidden states in the above variational interpretation can be estimated using an approximation that only requires propagating activations forward and backward, with pairs of layers learning to form a denoising auto-encoder. Finally, we extend the theory about the probabilistic interpretation of auto-encoders to justify improved sampling schemes based on the generative interpretation of denoising auto-encoders, and we validate all these ideas on generative learning tasks. | Towards Biologically Plausible Deep Learning | 2,827 |
We present a deep learning approach to estimation of the bead parameters in welding tasks. Our model is based on a four-hidden-layer neural network architecture. More specifically, the first three hidden layers of this architecture utilize Sigmoid function to produce their respective intermediate outputs. On the other hand, the last hidden layer uses a linear transformation to generate the final output of this architecture. This transforms our deep network architecture from a classifier to a non-linear regression model. We compare the performance of our deep network with a selected number of results in the literature to show a considerable improvement in reducing the errors in estimation of these values. Furthermore, we show its scalability on estimating the weld bead parameters with same level of accuracy on combination of datasets that pertain to different welding techniques. This is a nontrivial result that is counter-intuitive to the general belief in this field of research. | Application of Deep Neural Network in Estimation of the Weld Bead
Parameters | 2,828 |
The organizer of a machine learning competition faces the problem of maintaining an accurate leaderboard that faithfully represents the quality of the best submission of each competing team. What makes this estimation problem particularly challenging is its sequential and adaptive nature. As participants are allowed to repeatedly evaluate their submissions on the leaderboard, they may begin to overfit to the holdout data that supports the leaderboard. Few theoretical results give actionable advice on how to design a reliable leaderboard. Existing approaches therefore often resort to poorly understood heuristics such as limiting the bit precision of answers and the rate of re-submission. In this work, we introduce a notion of "leaderboard accuracy" tailored to the format of a competition. We introduce a natural algorithm called "the Ladder" and demonstrate that it simultaneously supports strong theoretical guarantees in a fully adaptive model of estimation, withstands practical adversarial attacks, and achieves high utility on real submission files from an actual competition hosted by Kaggle. Notably, we are able to sidestep a powerful recent hardness result for adaptive risk estimation that rules out algorithms such as ours under a seemingly very similar notion of accuracy. On a practical note, we provide a completely parameter-free variant of our algorithm that can be deployed in a real competition with no tuning required whatsoever. | The Ladder: A Reliable Leaderboard for Machine Learning Competitions | 2,829 |
Errors in data are usually unwelcome and so some means to correct them is useful. However, it is difficult to define, detect or correct errors in an unsupervised way. Here, we train a deep neural network to re-synthesize its inputs at its output layer for a given class of data. We then exploit the fact that this abstract transformation, which we call a deep transform (DT), inherently rejects information (errors) existing outside of the abstract feature space. Using the DT to perform probabilistic re-synthesis, we demonstrate the recovery of data that has been subject to extreme degradation. | Deep Transform: Error Correction via Probabilistic Re-Synthesis | 2,830 |
The majority of machine learning algorithms assumes that objects are represented as vectors. But often the objects we want to learn on are more naturally represented by other data structures such as sequences and time series. For these representations many standard learning algorithms are unavailable. We generalize gradient-based learning algorithms to time series under dynamic time warping. To this end, we introduce elastic functions, which extend functions on time series to matrix spaces. Necessary conditions are presented under which generalized gradient learning on time series is consistent. We indicate how results carry over to arbitrary elastic distance functions and to sequences consisting of symbolic elements. Specifically, four linear classifiers are extended to time series under dynamic time warping and applied to benchmark datasets. Results indicate that generalized gradient learning via elastic functions have the potential to complement the state-of-the-art in statistical pattern recognition on time series. | Generalized Gradient Learning on Time Series under Elastic
Transformations | 2,831 |
Motivated by the problem of computing investment portfolio weightings we investigate various methods of clustering as alternatives to traditional mean-variance approaches. Such methods can have significant benefits from a practical point of view since they remove the need to invert a sample covariance matrix, which can suffer from estimation error and will almost certainly be non-stationary. The general idea is to find groups of assets which share similar return characteristics over time and treat each group as a single composite asset. We then apply inverse volatility weightings to these new composite assets. In the course of our investigation we devise a method of clustering based on triangular potentials and we present associated theoretical results as well as various examples based on synthetic data. | Real time clustering of time series using triangular potentials | 2,832 |
Supervised classification approaches can predict labels for unknown data because of the supervised training process. The success of classification is heavily dependent on the labeled training data. Differently, clustering is effective in revealing the aggregation property of unlabeled data, but the performance of most clustering methods is limited by the absence of labeled data. In real applications, however, it is time-consuming and sometimes impossible to obtain labeled data. The combination of clustering and classification is a promising and active approach which can largely improve the performance. In this paper, we propose an innovative and effective clustering framework based on self-adaptive labeling (CSAL) which integrates clustering and classification on unlabeled data. Clustering is first employed to partition data and a certain proportion of clustered data are selected by our proposed labeling approach for training classifiers. In order to refine the trained classifiers, an iterative process of Expectation-Maximization algorithm is devised into the proposed clustering framework CSAL. Experiments are conducted on publicly data sets to test different combinations of clustering algorithms and classification models as well as various training data labeling methods. The experimental results show that our approach along with the self-adaptive method outperforms other methods. | CSAL: Self-adaptive Labeling based Clustering Integrating Supervised
Learning on Unlabeled Data | 2,833 |
In this paper we study the problem of learning from multiple modal data for purpose of document classification. In this problem, each document is composed two different modals of data, i.e., an image and a text. Cross-modal factor analysis (CFA) has been proposed to project the two different modals of data to a shared data space, so that the classification of a image or a text can be performed directly in this space. A disadvantage of CFA is that it has ignored the supervision information. In this paper, we improve CFA by incorporating the supervision information to represent and classify both image and text modals of documents. We project both image and text data to a shared data space by factor analysis, and then train a class label predictor in the shared space to use the class label information. The factor analysis parameter and the predictor parameter are learned jointly by solving one single objective function. With this objective function, we minimize the distance between the projections of image and text of the same document, and the classification error of the projection measured by hinge loss function. The objective function is optimized by an alternate optimization strategy in an iterative algorithm. Experiments in two different multiple modal document data sets show the advantage of the proposed algorithm over other CFA methods. | Supervised cross-modal factor analysis for multiple modal data
classification | 2,834 |
We describe an iterative procedure for optimizing policies, with guaranteed monotonic improvement. By making several approximations to the theoretically-justified procedure, we develop a practical algorithm, called Trust Region Policy Optimization (TRPO). This algorithm is similar to natural policy gradient methods and is effective for optimizing large nonlinear policies such as neural networks. Our experiments demonstrate its robust performance on a wide variety of tasks: learning simulated robotic swimming, hopping, and walking gaits; and playing Atari games using images of the screen as input. Despite its approximations that deviate from the theory, TRPO tends to give monotonic improvement, with little tuning of hyperparameters. | Trust Region Policy Optimization | 2,835 |
We study the classic online learning problem of predicting with expert advice, and propose a truly parameter-free and adaptive algorithm that achieves several objectives simultaneously without using any prior information. The main component of this work is an improved version of the NormalHedge.DT algorithm (Luo and Schapire, 2014), called AdaNormalHedge. On one hand, this new algorithm ensures small regret when the competitor has small loss and almost constant regret when the losses are stochastic. On the other hand, the algorithm is able to compete with any convex combination of the experts simultaneously, with a regret in terms of the relative entropy of the prior and the competitor. This resolves an open problem proposed by Chaudhuri et al. (2009) and Chernov and Vovk (2010). Moreover, we extend the results to the sleeping expert setting and provide two applications to illustrate the power of AdaNormalHedge: 1) competing with time-varying unknown competitors and 2) predicting almost as well as the best pruning tree. Our results on these applications significantly improve previous work from different aspects, and a special case of the first application resolves another open problem proposed by Warmuth and Koolen (2014) on whether one can simultaneously achieve optimal shifting regret for both adversarial and stochastic losses. | Achieving All with No Parameters: Adaptive NormalHedge | 2,836 |
Stochastic Dual Coordinate Ascent is a popular method for solving regularized loss minimization for the case of convex losses. In this paper we show how a variant of SDCA can be applied for non-convex losses. We prove linear convergence rate even if individual loss functions are non-convex as long as the expected loss is convex. | SDCA without Duality | 2,837 |
In this work we study the quantitative relation between VC-dimension and two other basic parameters related to learning and teaching. Namely, the quality of sample compression schemes and of teaching sets for classes of low VC-dimension. Let $C$ be a binary concept class of size $m$ and VC-dimension $d$. Prior to this work, the best known upper bounds for both parameters were $\log(m)$, while the best lower bounds are linear in $d$. We present significantly better upper bounds on both as follows. Set $k = O(d 2^d \log \log |C|)$. We show that there always exists a concept $c$ in $C$ with a teaching set (i.e. a list of $c$-labeled examples uniquely identifying $c$ in $C$) of size $k$. This problem was studied by Kuhlmann (1999). Our construction implies that the recursive teaching (RT) dimension of $C$ is at most $k$ as well. The RT-dimension was suggested by Zilles et al. and Doliwa et al. (2010). The same notion (under the name partial-ID width) was independently studied by Wigderson and Yehudayoff (2013). An upper bound on this parameter that depends only on $d$ is known just for the very simple case $d=1$, and is open even for $d=2$. We also make small progress towards this seemingly modest goal. We further construct sample compression schemes of size $k$ for $C$, with additional information of $k \log(k)$ bits. Roughly speaking, given any list of $C$-labelled examples of arbitrary length, we can retain only $k$ labeled examples in a way that allows to recover the labels of all others examples in the list, using additional $k\log (k)$ information bits. This problem was first suggested by Littlestone and Warmuth (1986). | Teaching and compressing for low VC-dimension | 2,838 |
We consider the problem of learning to choose actions using contextual information when provided with limited feedback in the form of relative pairwise comparisons. We study this problem in the dueling-bandits framework of Yue et al. (2009), which we extend to incorporate context. Roughly, the learner's goal is to find the best policy, or way of behaving, in some space of policies, although "best" is not always so clearly defined. Here, we propose a new and natural solution concept, rooted in game theory, called a von Neumann winner, a randomized policy that beats or ties every other policy. We show that this notion overcomes important limitations of existing solutions, particularly the Condorcet winner which has typically been used in the past, but which requires strong and often unrealistic assumptions. We then present three efficient algorithms for online learning in our setting, and for approximating a von Neumann winner from batch-like data. The first of these algorithms achieves particularly low regret, even when data is adversarial, although its time and space requirements are linear in the size of the policy space. The other two algorithms require time and space only logarithmic in the size of the policy space when provided access to an oracle for solving classification problems on the space. | Contextual Dueling Bandits | 2,839 |
A classic tension exists between exact inference in a simple model and approximate inference in a complex model. The latter offers expressivity and thus accuracy, but the former provides coverage of the space, an important property for confidence estimation and learning with indirect supervision. In this work, we introduce a new approach, reified context models, to reconcile this tension. Specifically, we let the amount of context (the arity of the factors in a graphical model) be chosen "at run-time" by reifying it---that is, letting this choice itself be a random variable inside the model. Empirically, we show that our approach obtains expressivity and coverage on three natural language tasks. | Reified Context Models | 2,840 |
Markov Chain Monte Carlo (MCMC) algorithms are often used for approximate inference inside learning, but their slow mixing can be difficult to diagnose and the approximations can seriously degrade learning. To alleviate these issues, we define a new model family using strong Doeblin Markov chains, whose mixing times can be precisely controlled by a parameter. We also develop an algorithm to learn such models, which involves maximizing the data likelihood under the induced stationary distribution of these chains. We show empirical improvements on two challenging inference tasks. | Learning Fast-Mixing Models for Structured Prediction | 2,841 |
Strongly adaptive algorithms are algorithms whose performance on every time interval is close to optimal. We present a reduction that can transform standard low-regret algorithms to strongly adaptive. As a consequence, we derive simple, yet efficient, strongly adaptive algorithms for a handful of problems. | Strongly Adaptive Online Learning | 2,842 |
Given a set $X$ and a function $h:X\longrightarrow\{0,1\}$ which labels each element of $X$ with either $0$ or $1$, we may define a function $h^{(s)}$ to measure the similarity of pairs of points in $X$ according to $h$. Specifically, for $h\in \{0,1\}^X$ we define $h^{(s)}\in \{0,1\}^{X\times X}$ by $h^{(s)}(w,x):= \mathbb{1}[h(w) = h(x)]$. This idea can be extended to a set of functions, or hypothesis space $\mathcal{H} \subseteq \{0,1\}^X$ by defining a similarity hypothesis space $\mathcal{H}^{(s)}:=\{h^{(s)}:h\in\mathcal{H}\}$. We show that ${{vc-dimension}}(\mathcal{H}^{(s)}) \in \Theta({{vc-dimension}}(\mathcal{H}))$. | The VC-Dimension of Similarity Hypotheses Spaces | 2,843 |
We study a general class of online learning problems where the feedback is specified by a graph. This class includes online prediction with expert advice and the multi-armed bandit problem, but also several learning problems where the online player does not necessarily observe his own loss. We analyze how the structure of the feedback graph controls the inherent difficulty of the induced $T$-round learning problem. Specifically, we show that any feedback graph belongs to one of three classes: strongly observable graphs, weakly observable graphs, and unobservable graphs. We prove that the first class induces learning problems with $\widetilde\Theta(\alpha^{1/2} T^{1/2})$ minimax regret, where $\alpha$ is the independence number of the underlying graph; the second class induces problems with $\widetilde\Theta(\delta^{1/3}T^{2/3})$ minimax regret, where $\delta$ is the domination number of a certain portion of the graph; and the third class induces problems with linear minimax regret. Our results subsume much of the previous work on learning with feedback graphs and reveal new connections to partial monitoring games. We also show how the regret is affected if the graphs are allowed to vary with time. | Online Learning with Feedback Graphs: Beyond Bandits | 2,844 |
Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the covariance matrices of these Gaussians. This learning problem arises in many areas ranging from the natural sciences to the social sciences, and has also found many machine learning applications. Unfortunately, learning mixture of Gaussians is an information theoretically hard problem: in order to learn the parameters up to a reasonable accuracy, the number of samples required is exponential in the number of Gaussian components in the worst case. In this work, we show that provided we are in high enough dimensions, the class of Gaussian mixtures is learnable in its most general form under a smoothed analysis framework, where the parameters are randomly perturbed from an adversarial starting point. In particular, given samples from a mixture of Gaussians with randomly perturbed parameters, when n > {\Omega}(k^2), we give an algorithm that learns the parameters with polynomial running time and using polynomial number of samples. The central algorithmic ideas consist of new ways to decompose the moment tensor of the Gaussian mixture by exploiting its structural properties. The symmetries of this tensor are derived from the combinatorial structure of higher order moments of Gaussian distributions (sometimes referred to as Isserlis' theorem or Wick's theorem). We also develop new tools for bounding smallest singular values of structured random matrices, which could be useful in other smoothed analysis settings. | Learning Mixtures of Gaussians in High Dimensions | 2,845 |
\emph{Semi-Automated Text Classification} (SATC) may be defined as the task of ranking a set $\mathcal{D}$ of automatically labelled textual documents in such a way that, if a human annotator validates (i.e., inspects and corrects where appropriate) the documents in a top-ranked portion of $\mathcal{D}$ with the goal of increasing the overall labelling accuracy of $\mathcal{D}$, the expected increase is maximized. An obvious SATC strategy is to rank $\mathcal{D}$ so that the documents that the classifier has labelled with the lowest confidence are top-ranked. In this work we show that this strategy is suboptimal. We develop new utility-theoretic ranking methods based on the notion of \emph{validation gain}, defined as the improvement in classification effectiveness that would derive by validating a given automatically labelled document. We also propose a new effectiveness measure for SATC-oriented ranking methods, based on the expected reduction in classification error brought about by partially validating a list generated by a given ranking method. We report the results of experiments showing that, with respect to the baseline method above, and according to the proposed measure, our utility-theoretic ranking methods can achieve substantially higher expected reductions in classification error. | Utility-Theoretic Ranking for Semi-Automated Text Classification | 2,846 |
We provide a simple and efficient algorithm for the projection operator for weighted $\ell_1$-norm regularization subject to a sum constraint, together with an elementary proof. The implementation of the proposed algorithm can be downloaded from the author's homepage. | An $\mathcal{O}(n\log n)$ projection operator for weighted $\ell_1$-norm
regularization with sum constraint | 2,847 |
We provide a simple and efficient algorithm for computing the Euclidean projection of a point onto the capped simplex---a simplex with an additional uniform bound on each coordinate---together with an elementary proof. Both the MATLAB and C++ implementations of the proposed algorithm can be downloaded at https://eng.ucmerced.edu/people/wwang5. | Projection onto the capped simplex | 2,848 |
This paper presents an unsupervised learning approach for simultaneous sample and feature selection, which is in contrast to existing works which mainly tackle these two problems separately. In fact the two tasks are often interleaved with each other: noisy and high-dimensional features will bring adverse effect on sample selection, while informative or representative samples will be beneficial to feature selection. Specifically, we propose a framework to jointly conduct active learning and feature selection based on the CUR matrix decomposition. From the data reconstruction perspective, both the selected samples and features can best approximate the original dataset respectively, such that the selected samples characterized by the features are highly representative. In particular, our method runs in one-shot without the procedure of iterative sample selection for progressive labeling. Thus, our model is especially suitable when there are few labeled samples or even in the absence of supervision, which is a particular challenge for existing methods. As the joint learning problem is NP-hard, the proposed formulation involves a convex but non-smooth optimization problem. We solve it efficiently by an iterative algorithm, and prove its global convergence. Experimental results on publicly available datasets corroborate the efficacy of our method compared with the state-of-the-art. | Joint Active Learning with Feature Selection via CUR Matrix
Decomposition | 2,849 |
We consider classification problems in which the label space has structure. A common example is hierarchical label spaces, corresponding to the case where one label subsumes another (e.g., animal subsumes dog). But labels can also be mutually exclusive (e.g., dog vs cat) or unrelated (e.g., furry, carnivore). To jointly model hierarchy and exclusion relations, the notion of a HEX (hierarchy and exclusion) graph was introduced in [7]. This combined a conditional random field (CRF) with a deep neural network (DNN), resulting in state of the art results when applied to visual object classification problems where the training labels were drawn from different levels of the ImageNet hierarchy (e.g., an image might be labeled with the basic level category "dog", rather than the more specific label "husky"). In this paper, we extend the HEX model to allow for soft or probabilistic relations between labels, which is useful when there is uncertainty about the relationship between two labels (e.g., an antelope is "sort of" furry, but not to the same degree as a grizzly bear). We call our new model pHEX, for probabilistic HEX. We show that the pHEX graph can be converted to an Ising model, which allows us to use existing off-the-shelf inference methods (in contrast to the HEX method, which needed specialized inference algorithms). Experimental results show significant improvements in a number of large-scale visual object classification tasks, outperforming the previous HEX model. | Probabilistic Label Relation Graphs with Ising Models | 2,850 |
The detection of very similar patterns in a time series, commonly called motifs, has received continuous and increasing attention from diverse scientific communities. In particular, recent approaches for discovering similar motifs of different lengths have been proposed. In this work, we show that such variable-length similarity-based motifs cannot be directly compared, and hence ranked, by their normalized dissimilarities. Specifically, we find that length-normalized motif dissimilarities still have intrinsic dependencies on the motif length, and that lowest dissimilarities are particularly affected by this dependency. Moreover, we find that such dependencies are generally non-linear and change with the considered data set and dissimilarity measure. Based on these findings, we propose a solution to rank those motifs and measure their significance. This solution relies on a compact but accurate model of the dissimilarity space, using a beta distribution with three parameters that depend on the motif length in a non-linear way. We believe the incomparability of variable-length dissimilarities could go beyond the field of time series, and that similar modeling strategies as the one used here could be of help in a more broad context. | Ranking and significance of variable-length similarity-based time series
motifs | 2,851 |
Polynomial kernel regression is one of the standard and state-of-the-art learning strategies. However, as is well known, the choices of the degree of polynomial kernel and the regularization parameter are still open in the realm of model selection. The first aim of this paper is to develop a strategy to select these parameters. On one hand, based on the worst-case learning rate analysis, we show that the regularization term in polynomial kernel regression is not necessary. In other words, the regularization parameter can decrease arbitrarily fast when the degree of the polynomial kernel is suitable tuned. On the other hand,taking account of the implementation of the algorithm, the regularization term is required. Summarily, the effect of the regularization term in polynomial kernel regression is only to circumvent the " ill-condition" of the kernel matrix. Based on this, the second purpose of this paper is to propose a new model selection strategy, and then design an efficient learning algorithm. Both theoretical and experimental analysis show that the new strategy outperforms the previous one. Theoretically, we prove that the new learning strategy is almost optimal if the regression function is smooth. Experimentally, it is shown that the new strategy can significantly reduce the computational burden without loss of generalization capability. | Model selection of polynomial kernel regression | 2,852 |
We resolve an open question from (Christiano, 2014b) posed in COLT'14 regarding the optimal dependency of the regret achievable for online local learning on the size of the label set. In this framework the algorithm is shown a pair of items at each step, chosen from a set of $n$ items. The learner then predicts a label for each item, from a label set of size $L$ and receives a real valued payoff. This is a natural framework which captures many interesting scenarios such as collaborative filtering, online gambling, and online max cut among others. (Christiano, 2014a) designed an efficient online learning algorithm for this problem achieving a regret of $O(\sqrt{nL^3T})$, where $T$ is the number of rounds. Information theoretically, one can achieve a regret of $O(\sqrt{n \log L T})$. One of the main open questions left in this framework concerns closing the above gap. In this work, we provide a complete answer to the question above via two main results. We show, via a tighter analysis, that the semi-definite programming based algorithm of (Christiano, 2014a), in fact achieves a regret of $O(\sqrt{nLT})$. Second, we show a matching computational lower bound. Namely, we show that a polynomial time algorithm for online local learning with lower regret would imply a polynomial time algorithm for the planted clique problem which is widely believed to be hard. We prove a similar hardness result under a related conjecture concerning planted dense subgraphs that we put forth. Unlike planted clique, the planted dense subgraph problem does not have any known quasi-polynomial time algorithms. Computational lower bounds for online learning are relatively rare, and we hope that the ideas developed in this work will lead to lower bounds for other online learning scenarios as well. | Label optimal regret bounds for online local learning | 2,853 |
Deep Neural Networks (DNNs) are analyzed via the theoretical framework of the information bottleneck (IB) principle. We first show that any DNN can be quantified by the mutual information between the layers and the input and output variables. Using this representation we can calculate the optimal information theoretic limits of the DNN and obtain finite sample generalization bounds. The advantage of getting closer to the theoretical limit is quantifiable both by the generalization bound and by the network's simplicity. We argue that both the optimal architecture, number of layers and features/connections at each layer, are related to the bifurcation points of the information bottleneck tradeoff, namely, relevant compression of the input layer with respect to the output layer. The hierarchical representations at the layered network naturally correspond to the structural phase transitions along the information curve. We believe that this new insight can lead to new optimality bounds and deep learning algorithms. | Deep Learning and the Information Bottleneck Principle | 2,854 |
The apsis toolkit presented in this paper provides a flexible framework for hyperparameter optimization and includes both random search and a bayesian optimizer. It is implemented in Python and its architecture features adaptability to any desired machine learning code. It can easily be used with common Python ML frameworks such as scikit-learn. Published under the MIT License other researchers are heavily encouraged to check out the code, contribute or raise any suggestions. The code can be found at github.com/FrederikDiehl/apsis. | apsis - Framework for Automated Optimization of Machine Learning Hyper
Parameters | 2,855 |
Time-series classification is an important problem for the data mining community due to the wide range of application domains involving time-series data. A recent paradigm, called shapelets, represents patterns that are highly predictive for the target variable. Shapelets are discovered by measuring the prediction accuracy of a set of potential (shapelet) candidates. The candidates typically consist of all the segments of a dataset, therefore, the discovery of shapelets is computationally expensive. This paper proposes a novel method that avoids measuring the prediction accuracy of similar candidates in Euclidean distance space, through an online clustering pruning technique. In addition, our algorithm incorporates a supervised shapelet selection that filters out only those candidates that improve classification accuracy. Empirical evidence on 45 datasets from the UCR collection demonstrate that our method is 3-4 orders of magnitudes faster than the fastest existing shapelet-discovery method, while providing better prediction accuracy. | Scalable Discovery of Time-Series Shapelets | 2,856 |
This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online. | LINE: Large-scale Information Network Embedding | 2,857 |
In this paper we introduce the idea of improving the performance of parametric temporal-difference (TD) learning algorithms by selectively emphasizing or de-emphasizing their updates on different time steps. In particular, we show that varying the emphasis of linear TD($\lambda$)'s updates in a particular way causes its expected update to become stable under off-policy training. The only prior model-free TD methods to achieve this with per-step computation linear in the number of function approximation parameters are the gradient-TD family of methods including TDC, GTD($\lambda$), and GQ($\lambda$). Compared to these methods, our _emphatic TD($\lambda$)_ is simpler and easier to use; it has only one learned parameter vector and one step-size parameter. Our treatment includes general state-dependent discounting and bootstrapping functions, and a way of specifying varying degrees of interest in accurately valuing different states. | An Emphatic Approach to the Problem of Off-policy Temporal-Difference
Learning | 2,858 |
Random Forest (RF) is an ensemble supervised machine learning technique that was developed by Breiman over a decade ago. Compared with other ensemble techniques, it has proved its accuracy and superiority. Many researchers, however, believe that there is still room for enhancing and improving its performance accuracy. This explains why, over the past decade, there have been many extensions of RF where each extension employed a variety of techniques and strategies to improve certain aspect(s) of RF. Since it has been proven empiricallthat ensembles tend to yield better results when there is a significant diversity among the constituent models, the objective of this paper is twofold. First, it investigates how data clustering (a well known diversity technique) can be applied to identify groups of similar decision trees in an RF in order to eliminate redundant trees by selecting a representative from each group (cluster). Second, these likely diverse representatives are then used to produce an extension of RF termed CLUB-DRF that is much smaller in size than RF, and yet performs at least as good as RF, and mostly exhibits higher performance in terms of accuracy. The latter refers to a known technique called ensemble pruning. Experimental results on 15 real datasets from the UCI repository prove the superiority of our proposed extension over the traditional RF. Most of our experiments achieved at least 95% or above pruning level while retaining or outperforming the RF accuracy. | On Extreme Pruning of Random Forest Ensembles for Real-time Predictive
Applications | 2,859 |
Time series shapelets are discriminative subsequences and their similarity to a time series can be used for time series classification. Since the discovery of time series shapelets is costly in terms of time, the applicability on long or multivariate time series is difficult. In this work we propose Ultra-Fast Shapelets that uses a number of random shapelets. It is shown that Ultra-Fast Shapelets yield the same prediction quality as current state-of-the-art shapelet-based time series classifiers that carefully select the shapelets by being by up to three orders of magnitudes. Since this method allows a ultra-fast shapelet discovery, using shapelets for long multivariate time series classification becomes feasible. A method for using shapelets for multivariate time series is proposed and Ultra-Fast Shapelets is proven to be successful in comparison to state-of-the-art multivariate time series classifiers on 15 multivariate time series datasets from various domains. Finally, time series derivatives that have proven to be useful for other time series classifiers are investigated for the shapelet-based classifiers. It is shown that they have a positive impact and that they are easy to integrate with a simple preprocessing step, without the need of adapting the shapelet discovery algorithm. | Ultra-Fast Shapelets for Time Series Classification | 2,860 |
Random Forest (RF) is an ensemble classification technique that was developed by Breiman over a decade ago. Compared with other ensemble techniques, it has proved its accuracy and superiority. Many researchers, however, believe that there is still room for enhancing and improving its performance in terms of predictive accuracy. This explains why, over the past decade, there have been many extensions of RF where each extension employed a variety of techniques and strategies to improve certain aspect(s) of RF. Since it has been proven empirically that ensembles tend to yield better results when there is a significant diversity among the constituent models, the objective of this paper is twofolds. First, it investigates how an unsupervised learning technique, namely, Local Outlier Factor (LOF) can be used to identify diverse trees in the RF. Second, trees with the highest LOF scores are then used to produce an extension of RF termed LOFB-DRF that is much smaller in size than RF, and yet performs at least as good as RF, but mostly exhibits higher performance in terms of accuracy. The latter refers to a known technique called ensemble pruning. Experimental results on 10 real datasets prove the superiority of our proposed extension over the traditional RF. Unprecedented pruning levels reaching 99% have been achieved at the time of boosting the predictive accuracy of the ensemble. The notably high pruning level makes the technique a good candidate for real-time applications. | An Outlier Detection-based Tree Selection Approach to Extreme Pruning of
Random Forests | 2,861 |
We introduce a novel training principle for probabilistic models that is an alternative to maximum likelihood. The proposed Generative Stochastic Networks (GSN) framework is based on learning the transition operator of a Markov chain whose stationary distribution estimates the data distribution. Because the transition distribution is a conditional distribution generally involving a small move, it has fewer dominant modes, being unimodal in the limit of small moves. Thus, it is easier to learn, more like learning to perform supervised function approximation, with gradients that can be obtained by back-propagation. The theorems provided here generalize recent work on the probabilistic interpretation of denoising auto-encoders and provide an interesting justification for dependency networks and generalized pseudolikelihood (along with defining an appropriate joint distribution and sampling mechanism, even when the conditionals are not consistent). We study how GSNs can be used with missing inputs and can be used to sample subsets of variables given the rest. Successful experiments are conducted, validating these theoretical results, on two image datasets and with a particular architecture that mimics the Deep Boltzmann Machine Gibbs sampler but allows training to proceed with backprop, without the need for layerwise pretraining. | GSNs : Generative Stochastic Networks | 2,862 |
We discuss data representation which can be learned automatically from data, are invariant to transformations, and at the same time selective, in the sense that two points have the same representation only if they are one the transformation of the other. The mathematical results here sharpen some of the key claims of i-theory -- a recent theory of feedforward processing in sensory cortex. | On Invariance and Selectivity in Representation Learning | 2,863 |
In this paper, we investigate a largely extended version of classical MAB problem, called networked combinatorial bandit problems. In particular, we consider the setting of a decision maker over a networked bandits as follows: each time a combinatorial strategy, e.g., a group of arms, is chosen, and the decision maker receives a reward resulting from her strategy and also receives a side bonus resulting from that strategy for each arm's neighbor. This is motivated by many real applications such as on-line social networks where friends can provide their feedback on shared content, therefore if we promote a product to a user, we can also collect feedback from her friends on that product. To this end, we consider two types of side bonus in this study: side observation and side reward. Upon the number of arms pulled at each time slot, we study two cases: single-play and combinatorial-play. Consequently, this leaves us four scenarios to investigate in the presence of side bonus: Single-play with Side Observation, Combinatorial-play with Side Observation, Single-play with Side Reward, and Combinatorial-play with Side Reward. For each case, we present and analyze a series of \emph{zero regret} polices where the expect of regret over time approaches zero as time goes to infinity. Extensive simulations validate the effectiveness of our results. | Networked Stochastic Multi-Armed Bandits with Combinatorial Strategies | 2,864 |
We analyse optimum reject strategies for prototype-based classifiers and real-valued rejection measures, using the distance of a data point to the closest prototype or probabilistic counterparts. We compare reject schemes with global thresholds, and local thresholds for the Voronoi cells of the classifier. For the latter, we develop a polynomial-time algorithm to compute optimum thresholds based on a dynamic programming scheme, and we propose an intuitive linear time, memory efficient approximation thereof with competitive accuracy. Evaluating the performance in various benchmarks, we conclude that local reject options are beneficial in particular for simple prototype-based classifiers, while the improvement is less pronounced for advanced models. For the latter, an accuracy-reject curve which is comparable to support vector machine classifiers with state of the art reject options can be reached. | Optimum Reject Options for Prototype-based Classification | 2,865 |
Predicting the Credit Defaulter is a perilous task of Financial Industries like Banks. Ascertaining non-payer before giving loan is a significant and conflict-ridden task of the Banker. Classification techniques are the better choice for predictive analysis like finding the claimant, whether he/she is an unpretentious customer or a cheat. Defining the outstanding classifier is a risky assignment for any industrialist like a banker. This allow computer science researchers to drill down efficient research works through evaluating different classifiers and finding out the best classifier for such predictive problems. This research work investigates the productivity of LADTree Classifier and REPTree Classifier for the credit risk prediction and compares their fitness through various measures. German credit dataset has been taken and used to predict the credit risk with a help of open source machine learning tool. | Proficiency Comparison of LADTree and REPTree Classifiers for Credit
Risk Forecast | 2,866 |
With the rapid increase in volume of time series medical data available through wearable devices, there is a need to employ automated algorithms to label data. Examples of labels include interventions, changes in activity (e.g. sleep) and changes in physiology (e.g. arrhythmias). However, automated algorithms tend to be unreliable resulting in lower quality care. Expert annotations are scarce, expensive, and prone to significant inter- and intra-observer variance. To address these problems, a Bayesian Continuous-valued Label Aggregator(BCLA) is proposed to provide a reliable estimation of label aggregation while accurately infer the precision and bias of each algorithm. The BCLA was applied to QT interval (pro-arrhythmic indicator) estimation from the electrocardiogram using labels from the 2006 PhysioNet/Computing in Cardiology Challenge database. It was compared to the mean, median, and a previously proposed Expectation Maximization (EM) label aggregation approaches. While accurately predicting each labelling algorithm's bias and precision, the root-mean-square error of the BCLA was 11.78$\pm$0.63ms, significantly outperforming the best Challenge entry (15.37$\pm$2.13ms) as well as the EM, mean, and median voting strategies (14.76$\pm$0.52ms, 17.61$\pm$0.55ms, and 14.43$\pm$0.57ms respectively with $p<0.0001$). | Fusing Continuous-valued Medical Labels using a Bayesian Model | 2,867 |
We give a probabilistic interpretation of sampling theory of graph signals. To do this, we first define a generative model for the data using a pairwise Gaussian random field (GRF) which depends on the graph. We show that, under certain conditions, reconstructing a graph signal from a subset of its samples by least squares is equivalent to performing MAP inference on an approximation of this GRF which has a low rank covariance matrix. We then show that a sampling set of given size with the largest associated cut-off frequency, which is optimal from a sampling theoretic point of view, minimizes the worst case predictive covariance of the MAP estimate on the GRF. This interpretation also gives an intuitive explanation for the superior performance of the sampling theoretic approach to active semi-supervised classification. | A Probabilistic Interpretation of Sampling Theory of Graph Signals | 2,868 |
In this paper, we propose the problem of online cost-sensitive clas- sifier adaptation and the first algorithm to solve it. We assume we have a base classifier for a cost-sensitive classification problem, but it is trained with respect to a cost setting different to the desired one. Moreover, we also have some training data samples streaming to the algorithm one by one. The prob- lem is to adapt the given base classifier to the desired cost setting using the steaming training samples online. To solve this problem, we propose to learn a new classifier by adding an adaptation function to the base classifier, and update the adaptation function parameter according to the streaming data samples. Given a input data sample and the cost of misclassifying it, we up- date the adaptation function parameter by minimizing cost weighted hinge loss and respecting previous learned parameter simultaneously. The proposed algorithm is compared to both online and off-line cost-sensitive algorithms on two cost-sensitive classification problems, and the experiments show that it not only outperforms them one classification performances, but also requires significantly less running time. | Online classifier adaptation for cost-sensitive learning | 2,869 |
Kernel Principal Component Analysis (KPCA) is a key machine learning algorithm for extracting nonlinear features from data. In the presence of a large volume of high dimensional data collected in a distributed fashion, it becomes very costly to communicate all of this data to a single data center and then perform kernel PCA. Can we perform kernel PCA on the entire dataset in a distributed and communication efficient fashion while maintaining provable and strong guarantees in solution quality? In this paper, we give an affirmative answer to the question by developing a communication efficient algorithm to perform kernel PCA in the distributed setting. The algorithm is a clever combination of subspace embedding and adaptive sampling techniques, and we show that the algorithm can take as input an arbitrary configuration of distributed datasets, and compute a set of global kernel principal components with relative error guarantees independent of the dimension of the feature space or the total number of data points. In particular, computing $k$ principal components with relative error $\epsilon$ over $s$ workers has communication cost $\tilde{O}(s \rho k/\epsilon+s k^2/\epsilon^3)$ words, where $\rho$ is the average number of nonzero entries in each data point. Furthermore, we experimented the algorithm with large-scale real world datasets and showed that the algorithm produces a high quality kernel PCA solution while using significantly less communication than alternative approaches. | Communication Efficient Distributed Kernel Principal Component Analysis | 2,870 |
In supervised learning, simple baseline classifiers can be constructed by only looking at the class, i.e., ignoring any other information from the dataset. The single-label learning community frequently uses as a reference the one which always predicts the majority class. Although a classifier might perform worse than this simple baseline classifier, this behaviour requires a special explanation. Aiming to motivate the community to compare experimental results with the ones provided by a multi-label baseline classifier, calling the attention about the need of special explanations related to classifiers which perform worse than the baseline, in this work we propose the use of General_B, a multi-label baseline classifier. General_B was evaluated in contrast to results published in the literature which were carefully selected using a systematic review process. It was found that a considerable number of published results on 10 frequently used datasets are worse than or equal to the ones obtained by General_B, and for one dataset it reaches up to 43% of the dataset published results. Moreover, although a simple baseline classifier was not considered in these publications, it was observed that even for very poor results no special explanations were provided in most of them. We hope that the findings of this work would encourage the multi-label community to consider the idea of using a simple baseline classifier, such that further explanations are provided when a classifiers performs worse than a baseline. | Comparing published multi-label classifier performance measures to the
ones obtained by a simple multi-label baseline classifier | 2,871 |
Sample compression schemes were defined by Littlestone and Warmuth (1986) as an abstraction of the structure underlying many learning algorithms. Roughly speaking, a sample compression scheme of size $k$ means that given an arbitrary list of labeled examples, one can retain only $k$ of them in a way that allows to recover the labels of all other examples in the list. They showed that compression implies PAC learnability for binary-labeled classes, and asked whether the other direction holds. We answer their question and show that every concept class $C$ with VC dimension $d$ has a sample compression scheme of size exponential in $d$. The proof uses an approximate minimax phenomenon for binary matrices of low VC dimension, which may be of interest in the context of game theory. | Sample compression schemes for VC classes | 2,872 |
Big Data concern large-volume, growing data sets that are complex and have multiple autonomous sources. Earlier technologies were not able to handle storage and processing of huge data thus Big Data concept comes into existence. This is a tedious job for users unstructured data. So, there should be some mechanism which classify unstructured data into organized form which helps user to easily access required data. Classification techniques over big transactional database provide required data to the users from large datasets more simple way. There are two main classification techniques, supervised and unsupervised. In this paper we focused on to study of different supervised classification techniques. Further this paper shows a advantages and limitations. | A Survey of Classification Techniques in the Area of Big Data | 2,873 |
Automated learning of patients demographics can be seen as multi-label problem where a patient model is based on different race and gender groups. The resulting model can be further integrated into Privacy-Preserving Data Mining, where it can be used to assess risk of identification of different patient groups. Our project considers relations between diabetes and demographics of patients as a multi-labelled problem. Most research in this area has been done as binary classification, where the target class is finding if a person has diabetes or not. But very few, and maybe no work has been done in multi-labeled analysis of the demographics of patients who are likely to be diagnosed with diabetes. To identify such groups, we applied ensembles of several multi-label learning algorithms. | Multi-Labeled Classification of Demographic Attributes of Patients: a
case study of diabetics patients | 2,874 |
Quasi-Newton methods are widely used in practise for convex loss minimization problems. These methods exhibit good empirical performance on a wide variety of tasks and enjoy super-linear convergence to the optimal solution. For large-scale learning problems, stochastic Quasi-Newton methods have been recently proposed. However, these typically only achieve sub-linear convergence rates and have not been shown to consistently perform well in practice since noisy Hessian approximations can exacerbate the effect of high-variance stochastic gradient estimates. In this work we propose Vite, a novel stochastic Quasi-Newton algorithm that uses an existing first-order technique to reduce this variance. Without exploiting the specific form of the approximate Hessian, we show that Vite reaches the optimum at a geometric rate with a constant step-size when dealing with smooth strongly convex functions. Empirically, we demonstrate improvements over existing stochastic Quasi-Newton and variance reduced stochastic gradient methods. | A Variance Reduced Stochastic Newton Method | 2,875 |
Multi-armed bandits (MAB) model sequential decision making problems, in which a learner sequentially chooses arms with unknown reward distributions in order to maximize its cumulative reward. Most of the prior work on MAB assumes that the reward distributions of each arm are independent. But in a wide variety of decision problems -- from drug dosage to dynamic pricing -- the expected rewards of different arms are correlated, so that selecting one arm provides information about the expected rewards of other arms as well. We propose and analyze a class of models of such decision problems, which we call {\em global bandits}. In the case in which rewards of all arms are deterministic functions of a single unknown parameter, we construct a greedy policy that achieves {\em bounded regret}, with a bound that depends on the single true parameter of the problem. Hence, this policy selects suboptimal arms only finitely many times with probability one. For this case we also obtain a bound on regret that is {\em independent of the true parameter}; this bound is sub-linear, with an exponent that depends on the informativeness of the arms. We also propose a variant of the greedy policy that achieves $\tilde{\mathcal{O}}(\sqrt{T})$ worst-case and $\mathcal{O}(1)$ parameter dependent regret. Finally, we perform experiments on dynamic pricing and show that the proposed algorithms achieve significant gains with respect to the well-known benchmarks. | Global Bandits | 2,876 |
Symmetric positive semi-definite (SPSD) matrix approximation methods have been extensively used to speed up large-scale eigenvalue computation and kernel learning methods. The standard sketch based method, which we call the prototype model, produces relatively accurate approximations, but is inefficient on large square matrices. The Nystr\"om method is highly efficient, but can only achieve low accuracy. In this paper we propose a novel model that we call the {\it fast SPSD matrix approximation model}. The fast model is nearly as efficient as the Nystr\"om method and as accurate as the prototype model. We show that the fast model can potentially solve eigenvalue problems and kernel learning problems in linear time with respect to the matrix size $n$ to achieve $1+\epsilon$ relative-error, whereas both the prototype model and the Nystr\"om method cost at least quadratic time to attain comparable error bound. Empirical comparisons among the prototype model, the Nystr\"om method, and our fast model demonstrate the superiority of the fast model. We also contribute new understandings of the Nystr\"om method. The Nystr\"om method is a special instance of our fast model and is approximation to the prototype model. Our technique can be straightforwardly applied to make the CUR matrix decomposition more efficiently computed without much affecting the accuracy. | Towards More Efficient SPSD Matrix Approximation and CUR Matrix
Decomposition | 2,877 |
Many modern multiclass and multilabel problems are characterized by increasingly large output spaces. For these problems, label embeddings have been shown to be a useful primitive that can improve computational and statistical efficiency. In this work we utilize a correspondence between rank constrained estimation and low dimensional label embeddings that uncovers a fast label embedding algorithm which works in both the multiclass and multilabel settings. The result is a randomized algorithm for partial least squares, whose running time is exponentially faster than naive algorithms. We demonstrate our techniques on two large-scale public datasets, from the Large Scale Hierarchical Text Challenge and the Open Directory Project, where we obtain state of the art results. | Fast Label Embeddings for Extremely Large Output Spaces | 2,878 |
Categorization axioms have been proposed to axiomatizing clustering results, which offers a hint of bridging the difference between human recognition system and machine learning through an intuitive observation: an object should be assigned to its most similar category. However, categorization axioms cannot be generalized into a general machine learning system as categorization axioms become trivial when the number of categories becomes one. In order to generalize categorization axioms into general cases, categorization input and categorization output are reinterpreted by inner and outer category representation. According to the categorization reinterpretation, two category representation axioms are presented. Category representation axioms and categorization axioms can be combined into a generalized categorization axiomatic framework, which accurately delimit the theoretical categorization constraints and overcome the shortcoming of categorization axioms. The proposed axiomatic framework not only discuses categorization test issue but also reinterprets many results in machine learning in a unified way, such as dimensionality reduction,density estimation, regression, clustering and classification. | Generalized Categorization Axioms | 2,879 |
Thompson sampling is one of the earliest randomized algorithms for multi-armed bandits (MAB). In this paper, we extend the Thompson sampling to Budgeted MAB, where there is random cost for pulling an arm and the total cost is constrained by a budget. We start with the case of Bernoulli bandits, in which the random rewards (costs) of an arm are independently sampled from a Bernoulli distribution. To implement the Thompson sampling algorithm in this case, at each round, we sample two numbers from the posterior distributions of the reward and cost for each arm, obtain their ratio, select the arm with the maximum ratio, and then update the posterior distributions. We prove that the distribution-dependent regret bound of this algorithm is $O(\ln B)$, where $B$ denotes the budget. By introducing a Bernoulli trial, we further extend this algorithm to the setting that the rewards (costs) are drawn from general distributions, and prove that its regret bound remains almost the same. Our simulation results demonstrate the effectiveness of the proposed algorithm. | Thompson Sampling for Budgeted Multi-armed Bandits | 2,880 |
Non-linear performance measures are widely used for the evaluation of learning algorithms. For example, $F$-measure is a commonly used performance measure for classification problems in machine learning and information retrieval community. We study the theoretical properties of a subset of non-linear performance measures called pseudo-linear performance measures which includes $F$-measure, \emph{Jaccard Index}, among many others. We establish that many notions of $F$-measures and \emph{Jaccard Index} are pseudo-linear functions of the per-class false negatives and false positives for binary, multiclass and multilabel classification. Based on this observation, we present a general reduction of such performance measure optimization problem to cost-sensitive classification problem with unknown costs. We then propose an algorithm with provable guarantees to obtain an approximately optimal classifier for the $F$-measure by solving a series of cost-sensitive classification problems. The strength of our analysis is to be valid on any dataset and any class of classifiers, extending the existing theoretical results on pseudo-linear measures, which are asymptotic in nature. We also establish the multi-objective nature of the $F$-score maximization problem by linking the algorithm with the weighted-sum approach used in multi-objective optimization. We present numerical experiments to illustrate the relative importance of cost asymmetry and thresholding when learning linear classifiers on various $F$-measure optimization tasks. | Theory of Optimizing Pseudolinear Performance Measures: Application to
F-measure | 2,881 |
Is he/she my type or not? The answer to this question depends on the personal preferences of the one asking it. The individual process of obtaining a full answer may generally be difficult and time consuming, but often an approximate answer can be obtained simply by looking at a photo of the potential match. Such approximate answers based on visual cues can be produced in a fraction of a second, a phenomenon that has led to a series of recently successful dating apps in which users rate others positively or negatively using primarily a single photo. In this paper we explore using convolutional networks to create a model of an individual's personal preferences based on rated photos. This introduced task is difficult due to the large number of variations in profile pictures and the noise in attractiveness labels. Toward this task we collect a dataset comprised of $9364$ pictures and binary labels for each. We compare performance of convolutional models trained in three ways: first directly on the collected dataset, second with features transferred from a network trained to predict gender, and third with features transferred from a network trained on ImageNet. Our findings show that ImageNet features transfer best, producing a model that attains $68.1\%$ accuracy on the test set and is moderately successful at predicting matches. | Can deep learning help you find the perfect match? | 2,882 |
The Neural Turing Machine (NTM) is more expressive than all previously considered models because of its external memory. It can be viewed as a broader effort to use abstract external Interfaces and to learn a parametric model that interacts with them. The capabilities of a model can be extended by providing it with proper Interfaces that interact with the world. These external Interfaces include memory, a database, a search engine, or a piece of software such as a theorem verifier. Some of these Interfaces are provided by the developers of the model. However, many important existing Interfaces, such as databases and search engines, are discrete. We examine feasibility of learning models to interact with discrete Interfaces. We investigate the following discrete Interfaces: a memory Tape, an input Tape, and an output Tape. We use a Reinforcement Learning algorithm to train a neural network that interacts with such Interfaces to solve simple algorithmic tasks. Our Interfaces are expressive enough to make our model Turing complete. | Reinforcement Learning Neural Turing Machines - Revised | 2,883 |
In order to speed-up classification models when facing a large number of categories, one usual approach consists in organizing the categories in a particular structure, this structure being then used as a way to speed-up the prediction computation. This is for example the case when using error-correcting codes or even hierarchies of categories. But in the majority of approaches, this structure is chosen \textit{by hand}, or during a preliminary step, and not integrated in the learning process. We propose a new model called Reinforced Decision Tree which simultaneously learns how to organize categories in a tree structure and how to classify any input based on this structure. This approach keeps the advantages of existing techniques (low inference complexity) but allows one to build efficient classifiers in one learning step. The learning algorithm is inspired by reinforcement learning and policy-gradient techniques which allows us to integrate the two steps (building the tree, and learning the classifier) in one single algorithm. | Reinforced Decision Trees | 2,884 |
Collectively, lung cancer, breast cancer and melanoma was diagnosed in over 535,340 people out of which, 209,400 deaths were reported [13]. It is estimated that over 600,000 people will be diagnosed with these forms of cancer in 2015. Most of the deaths from lung cancer, breast cancer and melanoma result due to late detection. All of these cancers, if detected early, are 100% curable. In this study, we develop and evaluate algorithms to diagnose Breast cancer, Melanoma, and Lung cancer. In the first part of the study, we employed a normalised Gradient Descent and an Artificial Neural Network to diagnose breast cancer with an overall accuracy of 91% and 95% respectively. In the second part of the study, an artificial neural network coupled with image processing and analysis algorithms was employed to achieve an overall accuracy of 93% A naive mobile based application that allowed people to take diagnostic tests on their phones was developed. Finally, a Support Vector Machine algorithm incorporating image processing and image analysis algorithms was developed to diagnose lung cancer with an accuracy of 94%. All of the aforementioned systems had very low false positive and false negative rates. We are developing an online network that incorporates all of these systems and allows people to collaborate globally. | A Comprehensive Study On The Applications Of Machine Learning For
Diagnosis Of Cancer | 2,885 |
In many naturally occurring optimization problems one needs to ensure that the definition of the optimization problem lends itself to solutions that are tractable to compute. In cases where exact solutions cannot be computed tractably, it is beneficial to have strong guarantees on the tractable approximate solutions. In order operate under these criterion most optimization problems are cast under the umbrella of convexity or submodularity. In this report we will study design and optimization over a common class of functions called submodular functions. Set functions, and specifically submodular set functions, characterize a wide variety of naturally occurring optimization problems, and the property of submodularity of set functions has deep theoretical consequences with wide ranging applications. Informally, the property of submodularity of set functions concerns the intuitive "principle of diminishing returns. This property states that adding an element to a smaller set has more value than adding it to a larger set. Common examples of submodular monotone functions are entropies, concave functions of cardinality, and matroid rank functions; non-monotone examples include graph cuts, network flows, and mutual information. In this paper we will review the formal definition of submodularity; the optimization of submodular functions, both maximization and minimization; and finally discuss some applications in relation to learning and reasoning using submodular functions. | Learning and Optimization with Submodular Functions | 2,886 |
Many real world data mining applications involve obtaining predictive models using data sets with strongly imbalanced distributions of the target variable. Frequently, the least common values of this target variable are associated with events that are highly relevant for end users (e.g. fraud detection, unusual returns on stock markets, anticipation of catastrophes, etc.). Moreover, the events may have different costs and benefits, which when associated with the rarity of some of them on the available training data creates serious problems to predictive modelling techniques. This paper presents a survey of existing techniques for handling these important applications of predictive analytics. Although most of the existing work addresses classification tasks (nominal target variables), we also describe methods designed to handle similar problems within regression tasks (numeric target variables). In this survey we discuss the main challenges raised by imbalanced distributions, describe the main approaches to these problems, propose a taxonomy of these methods and refer to some related problems within predictive modelling. | A Survey of Predictive Modelling under Imbalanced Distributions | 2,887 |
Metric learning aims to embed one metric space into another to benefit tasks like classification and clustering. Although a greatly distorted metric space has a high degree of freedom to fit training data, it is prone to overfitting and numerical inaccuracy. This paper presents {\it bounded-distortion metric learning} (BDML), a new metric learning framework which amounts to finding an optimal Mahalanobis metric space with a bounded-distortion constraint. An efficient solver based on the multiplicative weights update method is proposed. Moreover, we generalize BDML to pseudo-metric learning and devise the semidefinite relaxation and a randomized algorithm to approximately solve it. We further provide theoretical analysis to show that distortion is a key ingredient for stability and generalization ability of our BDML algorithm. Extensive experiments on several benchmark datasets yield promising results. | Bounded-Distortion Metric Learning | 2,888 |
Multi-task feature learning (MTFL) is a powerful technique in boosting the predictive performance by learning multiple related classification/regression/clustering tasks simultaneously. However, solving the MTFL problem remains challenging when the feature dimension is extremely large. In this paper, we propose a novel screening rule---that is based on the dual projection onto convex sets (DPC)---to quickly identify the inactive features---that have zero coefficients in the solution vectors across all tasks. One of the appealing features of DPC is that: it is safe in the sense that the detected inactive features are guaranteed to have zero coefficients in the solution vectors across all tasks. Thus, by removing the inactive features from the training phase, we may have substantial savings in the computational cost and memory usage without sacrificing accuracy. To the best of our knowledge, it is the first screening rule that is applicable to sparse models with multiple data matrices. A key challenge in deriving DPC is to solve a nonconvex problem. We show that we can solve for the global optimum efficiently via a properly chosen parametrization of the constraint set. Moreover, DPC has very low computational cost and can be integrated with any existing solvers. We have evaluated the proposed DPC rule on both synthetic and real data sets. The experiments indicate that DPC is very effective in identifying the inactive features---especially for high dimensional data---which leads to a speedup up to several orders of magnitude. | Safe Screening for Multi-Task Feature Learning with Multiple Data
Matrices | 2,889 |
Re-scale boosting (RBoosting) is a variant of boosting which can essentially improve the generalization performance of boosting learning. The key feature of RBoosting lies in introducing a shrinkage degree to re-scale the ensemble estimate in each gradient-descent step. Thus, the shrinkage degree determines the performance of RBoosting. The aim of this paper is to develop a concrete analysis concerning how to determine the shrinkage degree in $L_2$-RBoosting. We propose two feasible ways to select the shrinkage degree. The first one is to parameterize the shrinkage degree and the other one is to develope a data-driven approach of it. After rigorously analyzing the importance of the shrinkage degree in $L_2$-RBoosting learning, we compare the pros and cons of the proposed methods. We find that although these approaches can reach the same learning rates, the structure of the final estimate of the parameterized approach is better, which sometimes yields a better generalization capability when the number of sample is finite. With this, we recommend to parameterize the shrinkage degree of $L_2$-RBoosting. To this end, we present an adaptive parameter-selection strategy for shrinkage degree and verify its feasibility through both theoretical analysis and numerical verification. The obtained results enhance the understanding of RBoosting and further give guidance on how to use $L_2$-RBoosting for regression tasks. | Shrinkage degree in $L_2$-re-scale boosting for regression | 2,890 |
Several real-world classification problems are example-dependent cost-sensitive in nature, where the costs due to misclassification vary between examples and not only within classes. However, standard classification methods do not take these costs into account, and assume a constant cost of misclassification errors. In previous works, some methods that take into account the financial costs into the training of different algorithms have been proposed, with the example-dependent cost-sensitive decision tree algorithm being the one that gives the highest savings. In this paper we propose a new framework of ensembles of example-dependent cost-sensitive decision-trees. The framework consists in creating different example-dependent cost-sensitive decision trees on random subsamples of the training set, and then combining them using three different combination approaches. Moreover, we propose two new cost-sensitive combination approaches; cost-sensitive weighted voting and cost-sensitive stacking, the latter being based on the cost-sensitive logistic regression method. Finally, using five different databases, from four real-world applications: credit card fraud detection, churn modeling, credit scoring and direct marketing, we evaluate the proposed method against state-of-the-art example-dependent cost-sensitive techniques, namely, cost-proportionate sampling, Bayes minimum risk and cost-sensitive decision trees. The results show that the proposed algorithms have better results for all databases, in the sense of higher savings. | Ensemble of Example-Dependent Cost-Sensitive Decision Trees | 2,891 |
We study the problem of learning in the presence of a drifting target concept. Specifically, we provide bounds on the error rate at a given time, given a learner with access to a history of independent samples labeled according to a target concept that can change on each round. One of our main contributions is a refinement of the best previous results for polynomial-time algorithms for the space of linear separators under a uniform distribution. We also provide general results for an algorithm capable of adapting to a variable rate of drift of the target concept. Some of the results also describe an active learning variant of this setting, and provide bounds on the number of queries for the labels of points in the sequence sufficient to obtain the stated bounds on the error rates. | Learning with a Drifting Target Concept | 2,892 |
We study the optimal rates of convergence for estimating a prior distribution over a VC class from a sequence of independent data sets respectively labeled by independent target functions sampled from the prior. We specifically derive upper and lower bounds on the optimal rates under a smoothness condition on the correct prior, with the number of samples per data set equal the VC dimension. These results have implications for the improvements achievable via transfer learning. We additionally extend this setting to real-valued function, where we establish consistency of an estimator for the prior, and discuss an additional application to a preference elicitation problem in algorithmic economics. | Bounds on the Minimax Rate for Estimating a Prior over a VC Class from
Independent Learning Tasks | 2,893 |
Lifelong reinforcement learning provides a promising framework for developing versatile agents that can accumulate knowledge over a lifetime of experience and rapidly learn new tasks by building upon prior knowledge. However, current lifelong learning methods exhibit non-vanishing regret as the amount of experience increases and include limitations that can lead to suboptimal or unsafe control policies. To address these issues, we develop a lifelong policy gradient learner that operates in an adversarial set- ting to learn multiple tasks online while enforcing safety constraints on the learned policies. We demonstrate, for the first time, sublinear regret for lifelong policy search, and validate our algorithm on several benchmark dynamical systems and an application to quadrotor control. | Safe Policy Search for Lifelong Reinforcement Learning with Sublinear
Regret | 2,894 |
Although deep neural networks (DNN) are able to scale with direct advances in computational power (e.g., memory and processing speed), they are not well suited to exploit the recent trends for parallel architectures. In particular, gradient descent is a sequential process and the resulting serial dependencies mean that DNN training cannot be parallelized effectively. Here, we show that a DNN may be replicated over a massive parallel architecture and used to provide a cumulative sampling of local solution space which results in rapid and robust learning. We introduce a complimentary convolutional bootstrapping approach that enhances performance of the parallel architecture further. Our parallelized convolutional bootstrapping DNN out-performs an identical fully-trained traditional DNN after only a single iteration of training. | Instant Learning: Parallel Deep Neural Networks and Convolutional
Bootstrapping | 2,895 |
Real-world machine learning applications may require functions that are fast-to-evaluate and interpretable. In particular, guaranteed monotonicity of the learned function can be critical to user trust. We propose meeting these goals for low-dimensional machine learning problems by learning flexible, monotonic functions using calibrated interpolated look-up tables. We extend the structural risk minimization framework of lattice regression to train monotonic look-up tables by solving a convex problem with appropriate linear inequality constraints. In addition, we propose jointly learning interpretable calibrations of each feature to normalize continuous features and handle categorical or missing data, at the cost of making the objective non-convex. We address large-scale learning through parallelization, mini-batching, and propose random sampling of additive regularizer terms. Case studies with real-world problems with five to sixteen features and thousands to millions of training samples demonstrate the proposed monotonic functions can achieve state-of-the-art accuracy on practical problems while providing greater transparency to users. | Monotonic Calibrated Interpolated Look-Up Tables | 2,896 |
This paper addresses an important issue, known as sensor drift that behaves a nonlinear dynamic property in electronic nose (E-nose), from the viewpoint of machine learning. Traditional methods for drift compensation are laborious and costly due to the frequent acquisition and labeling process for gases samples recalibration. Extreme learning machines (ELMs) have been confirmed to be efficient and effective learning techniques for pattern recognition and regression. However, ELMs primarily focus on the supervised, semi-supervised and unsupervised learning problems in single domain (i.e. source domain). To our best knowledge, ELM with cross-domain learning capability has never been studied. This paper proposes a unified framework, referred to as Domain Adaptation Extreme Learning Machine (DAELM), which learns a robust classifier by leveraging a limited number of labeled data from target domain for drift compensation as well as gases recognition in E-nose systems, without loss of the computational efficiency and learning ability of traditional ELM. In the unified framework, two algorithms called DAELM-S and DAELM-T are proposed for the purpose of this paper, respectively. In order to percept the differences among ELM, DAELM-S and DAELM-T, two remarks are provided. Experiments on the popular sensor drift data with multiple batches collected by E-nose system clearly demonstrate that the proposed DAELM significantly outperforms existing drift compensation methods without cumbersome measures, and also bring new perspectives for ELM. | Domain Adaptation Extreme Learning Machines for Drift Compensation in
E-nose Systems | 2,897 |
This paper presents an algorithm for efficient training of sparse linear models with elastic net regularization. Extending previous work on delayed updates, the new algorithm applies stochastic gradient updates to non-zero features only, bringing weights current as needed with closed-form updates. Closed-form delayed updates for the $\ell_1$, $\ell_{\infty}$, and rarely used $\ell_2$ regularizers have been described previously. This paper provides closed-form updates for the popular squared norm $\ell^2_2$ and elastic net regularizers. We provide dynamic programming algorithms that perform each delayed update in constant time. The new $\ell^2_2$ and elastic net methods handle both fixed and varying learning rates, and both standard {stochastic gradient descent} (SGD) and {forward backward splitting (FoBoS)}. Experimental results show that on a bag-of-words dataset with $260,941$ features, but only $88$ nonzero features on average per training example, the dynamic programming method trains a logistic regression classifier with elastic net regularization over $2000$ times faster than otherwise. | Efficient Elastic Net Regularization for Sparse Linear Models | 2,898 |
Online learning has been in the spotlight from the machine learning society for a long time. To handle massive data in Big Data era, one single learner could never efficiently finish this heavy task. Hence, in this paper, we propose a novel distributed online learning algorithm to solve the problem. Comparing to typical centralized online learner, the distributed learners optimize their own learning parameters based on local data sources and timely communicate with neighbors. However, communication may lead to a privacy breach. Thus, we use differential privacy to preserve the privacy of learners, and study the influence of guaranteeing differential privacy on the utility of the distributed online learning algorithm. Furthermore, by using the results from Kakade and Tewari (2009), we use the regret bounds of online learning to achieve fast convergence rates for offline learning algorithms in distributed scenarios, which provides tighter utility performance than the existing state-of-the-art results. In simulation, we demonstrate that the differentially private offline learning algorithm has high variance, but we can use mini-batch to improve the performance. Finally, the simulations show that the analytical results of our proposed theorems are right and our private distributed online learning algorithm is a general framework. | Differentially Private Distributed Online Learning | 2,899 |
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