Pushing Stochastic Gradient towards Second-Order Methods -- Backpropagation Learning with Transformations in Nonlinearities

Recently, we proposed to transform the outputs of each hidden neuron in a multi-layer perceptron network to have zero output and zero slope on average, and use separate shortcut connections to model the linear dependencies instead. We continue the work by firstly introducing a third transformation to normalize the scale of the outputs of each hidden neuron, and secondly by analyzing the connections to second order optimization methods. We show that the transformations make a simple stochastic gradient behave closer to second-order optimization methods and thus speed up learning. This is shown both in theory and with experiments. The experiments on the third transformation show that while it further increases the speed of learning, it can also hurt performance by converging to a worse local optimum, where both the inputs and outputs of many hidden neurons are close to zero.


A Semantic Matching Energy Function for Learning with Multi-relational Data

Large-scale relational learning becomes crucial for handling the huge amounts of structured data generated daily in many application domains ranging from computational biology or information retrieval, to natural language processing. In this paper, we present a new neural network architecture designed to embed multi-relational graphs into a flexible continuous vector space in which the original data is kept and enhanced. The network is trained to encode the semantics of these graphs in order to assign high probabilities to plausible components. We empirically show that it reaches competitive performance in link prediction on standard datasets from the literature.


Learnable Pooling Regions for Image Classification

Biologically inspired, from the early HMAX model to Spatial Pyramid Matching, pooling has played an important role in visual recognition pipelines. Spatial pooling, by grouping of local codes, equips these methods with a certain degree of robustness to translation and deformation yet preserving important spatial information. Despite the predominance of this approach in current recognition systems, we have seen little progress to fully adapt the pooling strategy to the task at hand. This paper proposes a model for learning task dependent pooling scheme -- including previously proposed hand-crafted pooling schemes as a particular instantiation. In our work, we investigate the role of different regularization terms showing that the smooth regularization term is crucial to achieve strong performance using the presented architecture. Finally, we propose an efficient and parallel method to train the model. Our experiments show improved performance over hand-crafted pooling schemes on the CIFAR-10 and CIFAR-100 datasets -- in particular improving the state-of-the-art to 56.29% on the latter.


How good is the Electricity benchmark for evaluating concept drift adaptation

In this correspondence, we will point out a problem with testing adaptive classifiers on autocorrelated data. In such a case random change alarms may boost the accuracy figures. Hence, we cannot be sure if the adaptation is working well.


Block Coordinate Descent for Sparse NMF

Nonnegative matrix factorization (NMF) has become a ubiquitous tool for data analysis. An important variant is the sparse NMF problem which arises when we explicitly require the learnt features to be sparse. A natural measure of sparsity is the L$_0$ norm, however its optimization is NP-hard. Mixed norms, such as L$_1$/L$_2$ measure, have been shown to model sparsity robustly, based on intuitive attributes that such measures need to satisfy. This is in contrast to computationally cheaper alternatives such as the plain L$_1$ norm. However, present algorithms designed for optimizing the mixed norm L$_1$/L$_2$ are slow and other formulations for sparse NMF have been proposed such as those based on L$_1$ and L$_0$ norms. Our proposed algorithm allows us to solve the mixed norm sparsity constraints while not sacrificing computation time. We present experimental evidence on real-world datasets that shows our new algorithm performs an order of magnitude faster compared to the current state-of-the-art solvers optimizing the mixed norm and is suitable for large-scale datasets.


An Efficient Sufficient Dimension Reduction Method for Identifying Genetic Variants of Clinical Significance

Fast and cheaper next generation sequencing technologies will generate unprecedentedly massive and highly-dimensional genomic and epigenomic variation data. In the near future, a routine part of medical record will include the sequenced genomes. A fundamental question is how to efficiently extract genomic and epigenomic variants of clinical utility which will provide information for optimal wellness and interference strategies. Traditional paradigm for identifying variants of clinical validity is to test association of the variants. However, significantly associated genetic variants may or may not be usefulness for diagnosis and prognosis of diseases. Alternative to association studies for finding genetic variants of predictive utility is to systematically search variants that contain sufficient information for phenotype prediction. To achieve this, we introduce concepts of sufficient dimension reduction and coordinate hypothesis which project the original high dimensional data to very low dimensional space while preserving all information on response phenotypes. We then formulate clinically significant genetic variant discovery problem into sparse SDR problem and develop algorithms that can select significant genetic variants from up to or even ten millions of predictors with the aid of dividing SDR for whole genome into a number of subSDR problems defined for genomic regions. The sparse SDR is in turn formulated as sparse optimal scoring problem, but with penalty which can remove row vectors from the basis matrix. To speed up computation, we develop the modified alternating direction method for multipliers to solve the sparse optimal scoring problem which can easily be implemented in parallel. To illustrate its application, the proposed method is applied to simulation data and the NHLBI's Exome Sequencing Project dataset


The Neural Representation Benchmark and its Evaluation on Brain and Machine

A key requirement for the development of effective learning representations is their evaluation and comparison to representations we know to be effective. In natural sensory domains, the community has viewed the brain as a source of inspiration and as an implicit benchmark for success. However, it has not been possible to directly test representational learning algorithms directly against the representations contained in neural systems. Here, we propose a new benchmark for visual representations on which we have directly tested the neural representation in multiple visual cortical areas in macaque (utilizing data from [Majaj et al., 2012]), and on which any computer vision algorithm that produces a feature space can be tested. The benchmark measures the effectiveness of the neural or machine representation by computing the classification loss on the ordered eigendecomposition of a kernel matrix [Montavon et al., 2011]. In our analysis we find that the neural representation in visual area IT is superior to visual area V4. In our analysis of representational learning algorithms, we find that three-layer models approach the representational performance of V4 and the algorithm in [Le et al., 2012] surpasses the performance of V4. Impressively, we find that a recent supervised algorithm [Krizhevsky et al., 2012] achieves performance comparable to that of IT for an intermediate level of image variation difficulty, and surpasses IT at a higher difficulty level. We believe this result represents a major milestone: it is the first learning algorithm we have found that exceeds our current estimate of IT representation performance. We hope that this benchmark will assist the community in matching the representational performance of visual cortex and will serve as an initial rallying point for further correspondence between representations derived in brains and machines.


Sparse Penalty in Deep Belief Networks: Using the Mixed Norm Constraint

Deep Belief Networks (DBN) have been successfully applied on popular machine learning tasks. Specifically, when applied on hand-written digit recognition, DBNs have achieved approximate accuracy rates of 98.8%. In an effort to optimize the data representation achieved by the DBN and maximize their descriptive power, recent advances have focused on inducing sparse constraints at each layer of the DBN. In this paper we present a theoretical approach for sparse constraints in the DBN using the mixed norm for both non-overlapping and overlapping groups. We explore how these constraints affect the classification accuracy for digit recognition in three different datasets (MNIST, USPS, RIMES) and provide initial estimations of their usefulness by altering different parameters such as the group size and overlap percentage.


Learning Features with Structure-Adapting Multi-view Exponential Family Harmoniums

We proposea graphical model for multi-view feature extraction that automatically adapts its structure to achieve better representation of data distribution. The proposed model, structure-adapting multi-view harmonium (SA-MVH) has switch parameters that control the connection between hidden nodes and input views, and learn the switch parameter while training. Numerical experiments on synthetic and a real-world dataset demonstrate the useful behavior of the SA-MVH, compared to existing multi-view feature extraction methods.


Deep Predictive Coding Networks

The quality of data representation in deep learning methods is directly related to the prior model imposed on the representations; however, generally used fixed priors are not capable of adjusting to the context in the data. To address this issue, we propose deep predictive coding networks, a hierarchical generative model that empirically alters priors on the latent representations in a dynamic and context-sensitive manner. This model captures the temporal dependencies in time-varying signals and uses top-down information to modulate the representation in lower layers. The centerpiece of our model is a novel procedure to infer sparse states of a dynamic model which is used for feature extraction. We also extend this feature extraction block to introduce a pooling function that captures locally invariant representations. When applied on a natural video data, we show that our method is able to learn high-level visual features. We also demonstrate the role of the top-down connections by showing the robustness of the proposed model to structured noise.


Metric-Free Natural Gradient for Joint-Training of Boltzmann Machines

This paper introduces the Metric-Free Natural Gradient (MFNG) algorithm for training Boltzmann Machines. Similar in spirit to the Hessian-Free method of Martens [8], our algorithm belongs to the family of truncated Newton methods and exploits an efficient matrix-vector product to avoid explicitely storing the natural gradient metric $L$. This metric is shown to be the expected second derivative of the log-partition function (under the model distribution), or equivalently, the variance of the vector of partial derivatives of the energy function. We evaluate our method on the task of joint-training a 3-layer Deep Boltzmann Machine and show that MFNG does indeed have faster per-epoch convergence compared to Stochastic Maximum Likelihood with centering, though wall-clock performance is currently not competitive.


Information Theoretic Learning with Infinitely Divisible Kernels

In this paper, we develop a framework for information theoretic learning based on infinitely divisible matrices. We formulate an entropy-like functional on positive definite matrices based on Renyi's axiomatic definition of entropy and examine some key properties of this functional that lead to the concept of infinite divisibility. The proposed formulation avoids the plug in estimation of density and brings along the representation power of reproducing kernel Hilbert spaces. As an application example, we derive a supervised metric learning algorithm using a matrix based analogue to conditional entropy achieving results comparable with the state of the art.


Stochastic Pooling for Regularization of Deep Convolutional Neural Networks

We introduce a simple and effective method for regularizing large convolutional neural networks. We replace the conventional deterministic pooling operations with a stochastic procedure, randomly picking the activation within each pooling region according to a multinomial distribution, given by the activities within the pooling region. The approach is hyper-parameter free and can be combined with other regularization approaches, such as dropout and data augmentation. We achieve state-of-the-art performance on four image datasets, relative to other approaches that do not utilize data augmentation.


Joint Training Deep Boltzmann Machines for Classification

We introduce a new method for training deep Boltzmann machines jointly. Prior methods of training DBMs require an initial learning pass that trains the model greedily, one layer at a time, or do not perform well on classification tasks. In our approach, we train all layers of the DBM simultaneously, using a novel training procedure called multi-prediction training. The resulting model can either be interpreted as a single generative model trained to maximize a variational approximation to the generalized pseudolikelihood, or as a family of recurrent networks that share parameters and may be approximately averaged together using a novel technique we call the multi-inference trick. We show that our approach performs competitively for classification and outperforms previous methods in terms of accuracy of approximate inference and classification with missing inputs.


Kernelized Locality-Sensitive Hashing for Semi-Supervised Agglomerative Clustering

Large scale agglomerative clustering is hindered by computational burdens. We propose a novel scheme where exact inter-instance distance calculation is replaced by the Hamming distance between Kernelized Locality-Sensitive Hashing (KLSH) hashed values. This results in a method that drastically decreases computation time. Additionally, we take advantage of certain labeled data points via distance metric learning to achieve a competitive precision and recall comparing to K-Means but in much less computation time.


Saturating Auto-Encoders

We introduce a simple new regularizer for auto-encoders whose hidden-unit activation functions contain at least one zero-gradient (saturated) region. This regularizer explicitly encourages activations in the saturated region(s) of the corresponding activation function. We call these Saturating Auto-Encoders (SATAE). We show that the saturation regularizer explicitly limits the SATAE's ability to reconstruct inputs which are not near the data manifold. Furthermore, we show that a wide variety of features can be learned when different activation functions are used. Finally, connections are established with the Contractive and Sparse Auto-Encoders.


Big Neural Networks Waste Capacity

This article exposes the failure of some big neural networks to leverage added capacity to reduce underfitting. Past research suggest diminishing returns when increasing the size of neural networks. Our experiments on ImageNet LSVRC-2010 show that this may be due to the fact there are highly diminishing returns for capacity in terms of training error, leading to underfitting. This suggests that the optimization method - first order gradient descent - fails at this regime. Directly attacking this problem, either through the optimization method or the choices of parametrization, may allow to improve the generalization error on large datasets, for which a large capacity is required.


Revisiting Natural Gradient for Deep Networks

We evaluate natural gradient, an algorithm originally proposed in Amari (1997), for learning deep models. The contributions of this paper are as follows. We show the connection between natural gradient and three other recently proposed methods for training deep models: Hessian-Free (Martens, 2010), Krylov Subspace Descent (Vinyals and Povey, 2012) and TONGA (Le Roux et al., 2008). We describe how one can use unlabeled data to improve the generalization error obtained by natural gradient and empirically evaluate the robustness of the algorithm to the ordering of the training set compared to stochastic gradient descent. Finally we extend natural gradient to incorporate second order information alongside the manifold information and provide a benchmark of the new algorithm using a truncated Newton approach for inverting the metric matrix instead of using a diagonal approximation of it.


Deep Learning for Detecting Robotic Grasps

We consider the problem of detecting robotic grasps in an RGB-D view of a scene containing objects. In this work, we apply a deep learning approach to solve this problem, which avoids time-consuming hand-design of features. This presents two main challenges. First, we need to evaluate a huge number of candidate grasps. In order to make detection fast, as well as robust, we present a two-step cascaded structure with two deep networks, where the top detections from the first are re-evaluated by the second. The first network has fewer features, is faster to run, and can effectively prune out unlikely candidate grasps. The second, with more features, is slower but has to run only on the top few detections. Second, we need to handle multimodal inputs well, for which we present a method to apply structured regularization on the weights based on multimodal group regularization. We demonstrate that our method outperforms the previous state-of-the-art methods in robotic grasp detection, and can be used to successfully execute grasps on two different robotic platforms.


Feature Learning in Deep Neural Networks - Studies on Speech Recognition Tasks

Recent studies have shown that deep neural networks (DNNs) perform significantly better than shallow networks and Gaussian mixture models (GMMs) on large vocabulary speech recognition tasks. In this paper, we argue that the improved accuracy achieved by the DNNs is the result of their ability to extract discriminative internal representations that are robust to the many sources of variability in speech signals. We show that these representations become increasingly insensitive to small perturbations in the input with increasing network depth, which leads to better speech recognition performance with deeper networks. We also show that DNNs cannot extrapolate to test samples that are substantially different from the training examples. If the training data are sufficiently representative, however, internal features learned by the DNN are relatively stable with respect to speaker differences, bandwidth differences, and environment distortion. This enables DNN-based recognizers to perform as well or better than state-of-the-art systems based on GMMs or shallow networks without the need for explicit model adaptation or feature normalization.


Learning New Facts From Knowledge Bases With Neural Tensor Networks and Semantic Word Vectors

Knowledge bases provide applications with the benefit of easily accessible, systematic relational knowledge but often suffer in practice from their incompleteness and lack of knowledge of new entities and relations. Much work has focused on building or extending them by finding patterns in large unannotated text corpora. In contrast, here we mainly aim to complete a knowledge base by predicting additional true relationships between entities, based on generalizations that can be discerned in the given knowledgebase. We introduce a neural tensor network (NTN) model which predicts new relationship entries that can be added to the database. This model can be improved by initializing entity representations with word vectors learned in an unsupervised fashion from text, and when doing this, existing relations can even be queried for entities that were not present in the database. Our model generalizes and outperforms existing models for this problem, and can classify unseen relationships in WordNet with an accuracy of 75.8%.


Two SVDs produce more focal deep learning representations

A key characteristic of work on deep learning and neural networks in general is that it relies on representations of the input that support generalization, robust inference, domain adaptation and other desirable functionalities. Much recent progress in the field has focused on efficient and effective methods for computing representations. In this paper, we propose an alternative method that is more efficient than prior work and produces representations that have a property we call focality -- a property we hypothesize to be important for neural network representations. The method consists of a simple application of two consecutive SVDs and is inspired by Anandkumar (2012).


Behavior Pattern Recognition using A New Representation Model

We study the use of inverse reinforcement learning (IRL) as a tool for the recognition of agents' behavior on the basis of observation of their sequential decision behavior interacting with the environment. We model the problem faced by the agents as a Markov decision process (MDP) and model the observed behavior of the agents in terms of forward planning for the MDP. We use IRL to learn reward functions and then use these reward functions as the basis for clustering or classification models. Experimental studies with GridWorld, a navigation problem, and the secretary problem, an optimal stopping problem, suggest reward vectors found from IRL can be a good basis for behavior pattern recognition problems. Empirical comparisons of our method with several existing IRL algorithms and with direct methods that use feature statistics observed in state-action space suggest it may be superior for recognition problems.


Training Neural Networks with Stochastic Hessian-Free Optimization

Hessian-free (HF) optimization has been successfully used for training deep autoencoders and recurrent networks. HF uses the conjugate gradient algorithm to construct update directions through curvature-vector products that can be computed on the same order of time as gradients. In this paper we exploit this property and study stochastic HF with gradient and curvature mini-batches independent of the dataset size. We modify Martens' HF for these settings and integrate dropout, a method for preventing co-adaptation of feature detectors, to guard against overfitting. Stochastic Hessian-free optimization gives an intermediary between SGD and HF that achieves competitive performance on both classification and deep autoencoder experiments.


Regularized Discriminant Embedding for Visual Descriptor Learning

Images can vary according to changes in viewpoint, resolution, noise, and illumination. In this paper, we aim to learn representations for an image, which are robust to wide changes in such environmental conditions, using training pairs of matching and non-matching local image patches that are collected under various environmental conditions. We present a regularized discriminant analysis that emphasizes two challenging categories among the given training pairs: (1) matching, but far apart pairs and (2) non-matching, but close pairs in the original feature space (e.g., SIFT feature space). Compared to existing work on metric learning and discriminant analysis, our method can better distinguish relevant images from irrelevant, but look-alike images.


Zero-Shot Learning Through Cross-Modal Transfer

This work introduces a model that can recognize objects in images even if no training data is available for the objects. The only necessary knowledge about the unseen categories comes from unsupervised large text corpora. In our zero-shot framework distributional information in language can be seen as spanning a semantic basis for understanding what objects look like. Most previous zero-shot learning models can only differentiate between unseen classes. In contrast, our model can both obtain state of the art performance on classes that have thousands of training images and obtain reasonable performance on unseen classes. This is achieved by first using outlier detection in the semantic space and then two separate recognition models. Furthermore, our model does not require any manually defined semantic features for either words or images.


The IBMAP approach for Markov networks structure learning

In this work we consider the problem of learning the structure of Markov networks from data. We present an approach for tackling this problem called IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC algorithm, designed for avoiding important limitations of existing independence-based algorithms. These algorithms proceed by performing statistical independence tests on data, trusting completely the outcome of each test. In practice tests may be incorrect, resulting in potential cascading errors and the consequent reduction in the quality of the structures learned. IBMAP contemplates this uncertainty in the outcome of the tests through a probabilistic maximum-a-posteriori approach. The approach is instantiated in the IBMAP-HC algorithm, a structure selection strategy that performs a polynomial heuristic local search in the space of possible structures. We present an extensive empirical evaluation on synthetic and real data, showing that our algorithm outperforms significantly the current independence-based algorithms, in terms of data efficiency and quality of learned structures, with equivalent computational complexities. We also show the performance of IBMAP-HC in a real-world application of knowledge discovery: EDAs, which are evolutionary algorithms that use structure learning on each generation for modeling the distribution of populations. The experiments show that when IBMAP-HC is used to learn the structure, EDAs improve the convergence to the optimum.


Switched linear encoding with rectified linear autoencoders

Several recent results in machine learning have established formal connections between autoencoders---artificial neural network models that attempt to reproduce their inputs---and other coding models like sparse coding and K-means. This paper explores in depth an autoencoder model that is constructed using rectified linear activations on its hidden units. Our analysis builds on recent results to further unify the world of sparse linear coding models. We provide an intuitive interpretation of the behavior of these coding models and demonstrate this intuition using small, artificial datasets with known distributions.


Adaptive learning rates and parallelization for stochastic, sparse, non-smooth gradients

Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on stationary problems, and permitting learning rates to grow appropriately in non-stationary tasks. Here, we extend the idea in three directions, addressing proper minibatch parallelization, including reweighted updates for sparse or orthogonal gradients, improving robustness on non-smooth loss functions, in the process replacing the diagonal Hessian estimation procedure that may not always be available by a robust finite-difference approximation. The final algorithm integrates all these components, has linear complexity and is hyper-parameter free.


Discriminative Recurrent Sparse Auto-Encoders

We present the discriminative recurrent sparse auto-encoder model, comprising a recurrent encoder of rectified linear units, unrolled for a fixed number of iterations, and connected to two linear decoders that reconstruct the input and predict its supervised classification. Training via backpropagation-through-time initially minimizes an unsupervised sparse reconstruction error; the loss function is then augmented with a discriminative term on the supervised classification. The depth implicit in the temporally-unrolled form allows the system to exhibit all the power of deep networks, while substantially reducing the number of trainable parameters. From an initially unstructured network the hidden units differentiate into categorical-units, each of which represents an input prototype with a well-defined class; and part-units representing deformations of these prototypes. The learned organization of the recurrent encoder is hierarchical: part-units are driven directly by the input, whereas the activity of categorical-units builds up over time through interactions with the part-units. Even using a small number of hidden units per layer, discriminative recurrent sparse auto-encoders achieve excellent performance on MNIST.


Learning Output Kernels for Multi-Task Problems

Simultaneously solving multiple related learning tasks is beneficial under a variety of circumstances, but the prior knowledge necessary to correctly model task relationships is rarely available in practice. In this paper, we develop a novel kernel-based multi-task learning technique that automatically reveals structural inter-task relationships. Building over the framework of output kernel learning (OKL), we introduce a method that jointly learns multiple functions and a low-rank multi-task kernel by solving a non-convex regularization problem. Optimization is carried out via a block coordinate descent strategy, where each subproblem is solved using suitable conjugate gradient (CG) type iterative methods for linear operator equations. The effectiveness of the proposed approach is demonstrated on pharmacological and collaborative filtering data.


Reversible Jump MCMC Simulated Annealing for Neural Networks

We propose a novel reversible jump Markov chain Monte Carlo (MCMC) simulated annealing algorithm to optimize radial basis function (RBF) networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis functions. It performs a global search in the joint space of the parameters and number of parameters, thereby surmounting the problem of local minima. We also show that by calibrating a Bayesian model, we can obtain the classical AIC, BIC and MDL model selection criteria within a penalized likelihood framework. Finally, we show theoretically and empirically that the algorithm converges to the modes of the full posterior distribution in an efficient way.


Dynamic Bayesian Multinets

In this work, dynamic Bayesian multinets are introduced where a Markov chain state at time t determines conditional independence patterns between random variables lying within a local time window surrounding t. It is shown how information-theoretic criterion functions can be used to induce sparse, discriminative, and class-conditional network structures that yield an optimal approximation to the class posterior probability, and therefore are useful for the classification task. Using a new structure learning heuristic, the resulting models are tested on a medium-vocabulary isolated-word speech recognition task. It is demonstrated that these discriminatively structured dynamic Bayesian multinets, when trained in a maximum likelihood setting using EM, can outperform both HMMs and other dynamic Bayesian networks with a similar number of parameters.


Variational Relevance Vector Machines

The Support Vector Machine (SVM) of Vapnik (1998) has become widely established as one of the leading approaches to pattern recognition and machine learning. It expresses predictions in terms of a linear combination of kernel functions centred on a subset of the training data, known as support vectors. Despite its widespread success, the SVM suffers from some important limitations, one of the most significant being that it makes point predictions rather than generating predictive distributions. Recently Tipping (1999) has formulated the Relevance Vector Machine (RVM), a probabilistic model whose functional form is equivalent to the SVM. It achieves comparable recognition accuracy to the SVM, yet provides a full predictive distribution, and also requires substantially fewer kernel functions. The original treatment of the RVM relied on the use of type II maximum likelihood (the `evidence framework') to provide point estimates of the hyperparameters which govern model sparsity. In this paper we show how the RVM can be formulated and solved within a completely Bayesian paradigm through the use of variational inference, thereby giving a posterior distribution over both parameters and hyperparameters. We demonstrate the practicality and performance of the variational RVM using both synthetic and real world examples.


Utilities as Random Variables: Density Estimation and Structure Discovery

Decision theory does not traditionally include uncertainty over utility functions. We argue that the a person's utility value for a given outcome can be treated as we treat other domain attributes: as a random variable with a density function over its possible values. We show that we can apply statistical density estimation techniques to learn such a density function from a database of partially elicited utility functions. In particular, we define a Bayesian learning framework for this problem, assuming the distribution over utilities is a mixture of Gaussians, where the mixture components represent statistically coherent subpopulations. We can also extend our techniques to the problem of discovering generalized additivity structure in the utility functions in the population. We define a Bayesian model selection criterion for utility function structure and a search procedure over structures. The factorization of the utilities in the learned model, and the generalization obtained from density estimation, allows us to provide robust estimates of utilities using a significantly smaller number of utility elicitation questions. We experiment with our technique on synthetic utility data and on a real database of utility functions in the domain of prenatal diagnosis.


Bayesian Classification and Feature Selection from Finite Data Sets

Feature selection aims to select the smallest subset of features for a specified level of performance. The optimal achievable classification performance on a feature subset is summarized by its Receiver Operating Curve (ROC). When infinite data is available, the Neyman- Pearson (NP) design procedure provides the most efficient way of obtaining this curve. In practice the design procedure is applied to density estimates from finite data sets. We perform a detailed statistical analysis of the resulting error propagation on finite alphabets. We show that the estimated performance curve (EPC) produced by the design procedure is arbitrarily accurate given sufficient data, independent of the size of the feature set. However, the underlying likelihood ranking procedure is highly sensitive to errors that reduces the probability that the EPC is in fact the ROC. In the worst case, guaranteeing that the EPC is equal to the ROC may require data sizes exponential in the size of the feature set. These results imply that in theory the NP design approach may only be valid for characterizing relatively small feature subsets, even when the performance of any given classifier can be estimated very accurately. We discuss the practical limitations for on-line methods that ensures that the NP procedure operates in a statistically valid region.


Experiments with Random Projection

Recent theoretical work has identified random projection as a promising dimensionality reduction technique for learning mixtures of Gausians. Here we summarize these results and illustrate them by a wide variety of experiments on synthetic and real data.


A Two-round Variant of EM for Gaussian Mixtures

Given a set of possible models (e.g., Bayesian network structures) and a data sample, in the unsupervised model selection problem the task is to choose the most accurate model with respect to the domain joint probability distribution. In contrast to this, in supervised model selection it is a priori known that the chosen model will be used in the future for prediction tasks involving more ``focused' predictive distributions. Although focused predictive distributions can be produced from the joint probability distribution by marginalization, in practice the best model in the unsupervised sense does not necessarily perform well in supervised domains. In particular, the standard marginal likelihood score is a criterion for the unsupervised task, and, although frequently used for supervised model selection also, does not perform well in such tasks. In this paper we study the performance of the marginal likelihood score empirically in supervised Bayesian network selection tasks by using a large number of publicly available classification data sets, and compare the results to those obtained by alternative model selection criteria, including empirical crossvalidation methods, an approximation of a supervised marginal likelihood measure, and a supervised version of Dawids prequential(predictive sequential) principle.The results demonstrate that the marginal likelihood score does NOT perform well FOR supervised model selection, WHILE the best results are obtained BY using Dawids prequential r napproach.


Minimum Message Length Clustering Using Gibbs Sampling

The K-Mean and EM algorithms are popular in clustering and mixture modeling, due to their simplicity and ease of implementation. However, they have several significant limitations. Both coverage to a local optimum of their respective objective functions (ignoring the uncertainty in the model space), require the apriori specification of the number of classes/clsuters, and are inconsistent. In this work we overcome these limitations by using the Minimum Message Length (MML) principle and a variation to the K-Means/EM observation assignment and parameter calculation scheme. We maintain the simplicity of these approaches while constructing a Bayesian mixture modeling tool that samples/searches the model space using a Markov Chain Monte Carlo (MCMC) sampler known as a Gibbs sampler. Gibbs sampling allows us to visit each model according to its posterior probability. Therefore, if the model space is multi-modal we will visit all models and not get stuck in local optima. We call our approach multiple chains at equilibrium (MCE) MML sampling.


Mix-nets: Factored Mixtures of Gaussians in Bayesian Networks With Mixed Continuous And Discrete Variables

Recently developed techniques have made it possible to quickly learn accurate probability density functions from data in low-dimensional continuous space. In particular, mixtures of Gaussians can be fitted to data very quickly using an accelerated EM algorithm that employs multiresolution kd-trees (Moore, 1999). In this paper, we propose a kind of Bayesian networks in which low-dimensional mixtures of Gaussians over different subsets of the domain's variables are combined into a coherent joint probability model over the entire domain. The network is also capable of modeling complex dependencies between discrete variables and continuous variables without requiring discretization of the continuous variables. We present efficient heuristic algorithms for automatically learning these networks from data, and perform comparative experiments illustrated how well these networks model real scientific data and synthetic data. We also briefly discuss some possible improvements to the networks, as well as possible applications.


Rao-Blackwellised Particle Filtering for Dynamic Bayesian Networks

Particle filters (PFs) are powerful sampling-based inference/learning algorithms for dynamic Bayesian networks (DBNs). They allow us to treat, in a principled way, any type of probability distribution, nonlinearity and non-stationarity. They have appeared in several fields under such names as "condensation", "sequential Monte Carlo" and "survival of the fittest". In this paper, we show how we can exploit the structure of the DBN to increase the efficiency of particle filtering, using a technique known as Rao-Blackwellisation. Essentially, this samples some of the variables, and marginalizes out the rest exactly, using the Kalman filter, HMM filter, junction tree algorithm, or any other finite dimensional optimal filter. We show that Rao-Blackwellised particle filters (RBPFs) lead to more accurate estimates than standard PFs. We demonstrate RBPFs on two problems, namely non-stationary online regression with radial basis function networks and robot localization and map building. We also discuss other potential application areas and provide references to some finite dimensional optimal filters.


Learning Graphical Models of Images, Videos and Their Spatial Transformations

Mixtures of Gaussians, factor analyzers (probabilistic PCA) and hidden Markov models are staples of static and dynamic data modeling and image and video modeling in particular. We show how topographic transformations in the input, such as translation and shearing in images, can be accounted for in these models by including a discrete transformation variable. The resulting models perform clustering, dimensionality reduction and time-series analysis in a way that is invariant to transformations in the input. Using the EM algorithm, these transformation-invariant models can be fit to static data and time series. We give results on filtering microscopy images, face and facial pose clustering, handwritten digit modeling and recognition, video clustering, object tracking, and removal of distractions from video sequences.


Being Bayesian about Network Structure

In many domains, we are interested in analyzing the structure of the underlying distribution, e.g., whether one variable is a direct parent of the other. Bayesian model-selection attempts to find the MAP model and use its structure to answer these questions. However, when the amount of available data is modest, there might be many models that have non-negligible posterior. Thus, we want compute the Bayesian posterior of a feature, i.e., the total posterior probability of all models that contain it. In this paper, we propose a new approach for this task. We first show how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed ordering over network variables. This allows us to compute, for a given ordering, both the marginal probability of the data and the posterior of a feature. We then use this result as the basis for an algorithm that approximates the Bayesian posterior of a feature. Our approach uses a Markov Chain Monte Carlo (MCMC) method, but over orderings rather than over network structures. The space of orderings is much smaller and more regular than the space of structures, and has a smoother posterior `landscape'. We present empirical results on synthetic and real-life datasets that compare our approach to full model averaging (when possible), to MCMC over network structures, and to a non-Bayesian bootstrap approach.


Gaussian Process Networks

In this paper we address the problem of learning the structure of a Bayesian network in domains with continuous variables. This task requires a procedure for comparing different candidate structures. In the Bayesian framework, this is done by evaluating the {em marginal likelihood/} of the data given a candidate structure. This term can be computed in closed-form for standard parametric families (e.g., Gaussians), and can be approximated, at some computational cost, for some semi-parametric families (e.g., mixtures of Gaussians). We present a new family of continuous variable probabilistic networks that are based on {em Gaussian Process/} priors. These priors are semi-parametric in nature and can learn almost arbitrary noisy functional relations. Using these priors, we can directly compute marginal likelihoods for structure learning. The resulting method can discover a wide range of functional dependencies in multivariate data. We develop the Bayesian score of Gaussian Process Networks and describe how to learn them from data. We present empirical results on artificial data as well as on real-life domains with non-linear dependencies.


Inference for Belief Networks Using Coupling From the Past

Inference for belief networks using Gibbs sampling produces a distribution for unobserved variables that differs from the correct distribution by a (usually) unknown error, since convergence to the right distribution occurs only asymptotically. The method of "coupling from the past" samples from exactly the correct distribution by (conceptually) running dependent Gibbs sampling simulations from every possible starting state from a time far enough in the past that all runs reach the same state at time t=0. Explicitly considering every possible state is intractable for large networks, however. We propose a method for layered noisy-or networks that uses a compact, but often imprecise, summary of a set of states. This method samples from exactly the correct distribution, and requires only about twice the time per step as ordinary Gibbs sampling, but it may require more simulation steps than would be needed if chains were tracked exactly.


Dependency Networks for Collaborative Filtering and Data Visualization

We describe a graphical model for probabilistic relationships---an alternative to the Bayesian network---called a dependency network. The graph of a dependency network, unlike a Bayesian network, is potentially cyclic. The probability component of a dependency network, like a Bayesian network, is a set of conditional distributions, one for each node given its parents. We identify several basic properties of this representation and describe a computationally efficient procedure for learning the graph and probability components from data. We describe the application of this representation to probabilistic inference, collaborative filtering (the task of predicting preferences), and the visualization of acausal predictive relationships.


Feature Selection and Dualities in Maximum Entropy Discrimination

Incorporating feature selection into a classification or regression method often carries a number of advantages. In this paper we formalize feature selection specifically from a discriminative perspective of improving classification/regression accuracy. The feature selection method is developed as an extension to the recently proposed maximum entropy discrimination (MED) framework. We describe MED as a flexible (Bayesian) regularization approach that subsumes, e.g., support vector classification, regression and exponential family models. For brevity, we restrict ourselves primarily to feature selection in the context of linear classification/regression methods and demonstrate that the proposed approach indeed carries substantial improvements in practice. Moreover, we discuss and develop various extensions of feature selection, including the problem of dealing with example specific but unobserved degrees of freedom -- alignments or invariants.


Tractable Bayesian Learning of Tree Belief Networks

In this paper we present decomposable priors, a family of priors over structure and parameters of tree belief nets for which Bayesian learning with complete observations is tractable, in the sense that the posterior is also decomposable and can be completely determined analytically in polynomial time. This follows from two main results: First, we show that factored distributions over spanning trees in a graph can be integrated in closed form. Second, we examine priors over tree parameters and show that a set of assumptions similar to (Heckerman and al. 1995) constrain the tree parameter priors to be a compactly parameterized product of Dirichlet distributions. Beside allowing for exact Bayesian learning, these results permit us to formulate a new class of tractable latent variable models in which the likelihood of a data point is computed through an ensemble average over tree structures.


The Anchors Hierachy: Using the triangle inequality to survive high dimensional data

This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions, decorating kd-trees with additional "cached sufficient statistics" such as first and second moments and contingency tables can provide satisfying acceleration for a very wide range of statistical learning tasks such as kernel regression, locally weighted regression, k-means clustering, mixture modeling and Bayes Net learning. In this paper, we begin by defining the anchors hierarchy - a fast data structure and algorithm for localizing data based only on a triangle-inequality-obeying distance metric. We show how this, in its own right, gives a fast and effective clustering of data. But more importantly we show how it can produce a well-balanced structure similar to a Ball-Tree (Omohundro, 1991) or a kind of metric tree (Uhlmann, 1991; Ciaccia, Patella, & Zezula, 1997) in a way that is neither "top-down" nor "bottom-up" but instead "middle-out". We then show how this structure, decorated with cached sufficient statistics, allows a wide variety of statistical learning algorithms to be accelerated even in thousands of dimensions.


PEGASUS: A Policy Search Method for Large MDPs and POMDPs

We propose a new approach to the problem of searching a space of policies for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP), given a model. Our approach is based on the following observation: Any (PO)MDP can be transformed into an "equivalent" POMDP in which all state transitions (given the current state and action) are deterministic. This reduces the general problem of policy search to one in which we need only consider POMDPs with deterministic transitions. We give a natural way of estimating the value of all policies in these transformed POMDPs. Policy search is then simply performed by searching for a policy with high estimated value. We also establish conditions under which our value estimates will be good, recovering theoretical results similar to those of Kearns, Mansour and Ng (1999), but with "sample complexity" bounds that have only a polynomial rather than exponential dependence on the horizon time. Our method applies to arbitrary POMDPs, including ones with infinite state and action spaces. We also present empirical results for our approach on a small discrete problem, and on a complex continuous state/continuous action problem involving learning to ride a bicycle.


Adaptive Importance Sampling for Estimation in Structured Domains

Sampling is an important tool for estimating large, complex sums and integrals over high dimensional spaces. For instance, important sampling has been used as an alternative to exact methods for inference in belief networks. Ideally, we want to have a sampling distribution that provides optimal-variance estimators. In this paper, we present methods that improve the sampling distribution by systematically adapting it as we obtain information from the samples. We present a stochastic-gradient-descent method for sequentially updating the sampling distribution based on the direct minization of the variance. We also present other stochastic-gradient-descent methods based on the minimizationof typical notions of distance between the current sampling distribution and approximations of the target, optimal distribution. We finally validate and compare the different methods empirically by applying them to the problem of action evaluation in influence diagrams.


Monte Carlo Inference via Greedy Importance Sampling

We present a new method for conducting Monte Carlo inference in graphical models which combines explicit search with generalized importance sampling. The idea is to reduce the variance of importance sampling by searching for significant points in the target distribution. We prove that it is possible to introduce search and still maintain unbiasedness. We then demonstrate our procedure on a few simple inference tasks and show that it can improve the inference quality of standard MCMC methods, including Gibbs sampling, Metropolis sampling, and Hybrid Monte Carlo. This paper extends previous work which showed how greedy importance sampling could be correctly realized in the one-dimensional case.


Combining Feature and Prototype Pruning by Uncertainty Minimization

We focus in this paper on dataset reduction techniques for use in k-nearest neighbor classification. In such a context, feature and prototype selections have always been independently treated by the standard storage reduction algorithms. While this certifying is theoretically justified by the fact that each subproblem is NP-hard, we assume in this paper that a joint storage reduction is in fact more intuitive and can in practice provide better results than two independent processes. Moreover, it avoids a lot of distance calculations by progressively removing useless instances during the feature pruning. While standard selection algorithms often optimize the accuracy to discriminate the set of solutions, we use in this paper a criterion based on an uncertainty measure within a nearest-neighbor graph. This choice comes from recent results that have proven that accuracy is not always the suitable criterion to optimize. In our approach, a feature or an instance is removed if its deletion improves information of the graph. Numerous experiments are presented in this paper and a statistical analysis shows the relevance of our approach, and its tolerance in the presence of noise.


Dynamic Trees: A Structured Variational Method Giving Efficient Propagation Rules

Dynamic trees are mixtures of tree structured belief networks. They solve some of the problems of fixed tree networks at the cost of making exact inference intractable. For this reason approximate methods such as sampling or mean field approaches have been used. However, mean field approximations assume a factorized distribution over node states. Such a distribution seems unlickely in the posterior, as nodes are highly correlated in the prior. Here a structured variational approach is used, where the posterior distribution over the non-evidential nodes is itself approximated by a dynamic tree. It turns out that this form can be used tractably and efficiently. The result is a set of update rules which can propagate information through the network to obtain both a full variational approximation, and the relevant marginals. The progagtion rules are more efficient than the mean field approach and give noticeable quantitative and qualitative improvement in the inference. The marginals calculated give better approximations to the posterior than loopy propagation on a small toy problem.


An Uncertainty Framework for Classification

We define a generalized likelihood function based on uncertainty measures and show that maximizing such a likelihood function for different measures induces different types of classifiers. In the probabilistic framework, we obtain classifiers that optimize the cross-entropy function. In the possibilistic framework, we obtain classifiers that maximize the interclass margin. Furthermore, we show that the support vector machine is a sub-class of these maximum-margin classifiers.


A Branch-and-Bound Algorithm for MDL Learning Bayesian Networks

This paper extends the work in [Suzuki, 1996] and presents an efficient depth-first branch-and-bound algorithm for learning Bayesian network structures, based on the minimum description length (MDL) principle, for a given (consistent) variable ordering. The algorithm exhaustively searches through all network structures and guarantees to find the network with the best MDL score. Preliminary experiments show that the algorithm is efficient, and that the time complexity grows slowly with the sample size. The algorithm is useful for empirically studying both the performance of suboptimal heuristic search algorithms and the adequacy of the MDL principle in learning Bayesian networks.


Model-Based Hierarchical Clustering

We present an approach to model-based hierarchical clustering by formulating an objective function based on a Bayesian analysis. This model organizes the data into a cluster hierarchy while specifying a complex feature-set partitioning that is a key component of our model. Features can have either a unique distribution in every cluster or a common distribution over some (or even all) of the clusters. The cluster subsets over which these features have such a common distribution correspond to the nodes (clusters) of the tree representing the hierarchy. We apply this general model to the problem of document clustering for which we use a multinomial likelihood function and Dirichlet priors. Our algorithm consists of a two-stage process wherein we first perform a flat clustering followed by a modified hierarchical agglomerative merging process that includes determining the features that will have common distributions over the merged clusters. The regularization induced by using the marginal likelihood automatically determines the optimal model structure including number of clusters, the depth of the tree and the subset of features to be modeled as having a common distribution at each node. We present experimental results on both synthetic data and a real document collection.


Variational Approximations between Mean Field Theory and the Junction Tree Algorithm

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generalized mean field equations to optimize the cluster potentials. We show that the method bridges the gap between the standard mean field approximation and the exact junction tree algorithm. In addition, we address the problem of how to choose the graphical structure of the approximating distribution. From the generalised mean field equations we derive rules to simplify the structure of the approximating distribution in advance without affecting the quality of the approximation. We also show how the method fits into some other variational approximations that are currently popular.


Efficient Sample Reuse in Policy Gradients with Parameter-based Exploration

The policy gradient approach is a flexible and powerful reinforcement learning method particularly for problems with continuous actions such as robot control. A common challenge in this scenario is how to reduce the variance of policy gradient estimates for reliable policy updates. In this paper, we combine the following three ideas and give a highly effective policy gradient method: (a) the policy gradients with parameter based exploration, which is a recently proposed policy search method with low variance of gradient estimates, (b) an importance sampling technique, which allows us to reuse previously gathered data in a consistent way, and (c) an optimal baseline, which minimizes the variance of gradient estimates with their unbiasedness being maintained. For the proposed method, we give theoretical analysis of the variance of gradient estimates and show its usefulness through extensive experiments.


Knowledge Matters: Importance of Prior Information for Optimization

We explore the effect of introducing prior information into the intermediate level of neural networks for a learning task on which all the state-of-the-art machine learning algorithms tested failed to learn. We motivate our work from the hypothesis that humans learn such intermediate concepts from other individuals via a form of supervision or guidance using a curriculum. The experiments we have conducted provide positive evidence in favor of this hypothesis. In our experiments, a two-tiered MLP architecture is trained on a dataset with 64x64 binary inputs images, each image with three sprites. The final task is to decide whether all the sprites are the same or one of them is different. Sprites are pentomino tetris shapes and they are placed in an image with different locations using scaling and rotation transformations. The first part of the two-tiered MLP is pre-trained with intermediate-level targets being the presence of sprites at each location, while the second part takes the output of the first part as input and predicts the final task's target binary event. The two-tiered MLP architecture, with a few tens of thousand examples, was able to learn the task perfectly, whereas all other algorithms (include unsupervised pre-training, but also traditional algorithms like SVMs, decision trees and boosting) all perform no better than chance. We hypothesize that the optimization difficulty involved when the intermediate pre-training is not performed is due to the {\em composition} of two highly non-linear tasks. Our findings are also consistent with hypotheses on cultural learning inspired by the observations of optimization problems with deep learning, presumably because of effective local minima.


On the Product Rule for Classification Problems

We discuss theoretical aspects of the product rule for classification problems in supervised machine learning for the case of combining classifiers. We show that (1) the product rule arises from the MAP classifier supposing equivalent priors and conditional independence given a class; (2) under some conditions, the product rule is equivalent to minimizing the sum of the squared distances to the respective centers of the classes related with different features, such distances being weighted by the spread of the classes; (3) observing some hypothesis, the product rule is equivalent to concatenating the vectors of features.


Herded Gibbs Sampling

The Gibbs sampler is one of the most popular algorithms for inference in statistical models. In this paper, we introduce a herding variant of this algorithm, called herded Gibbs, that is entirely deterministic. We prove that herded Gibbs has an $O(1/T)$ convergence rate for models with independent variables and for fully connected probabilistic graphical models. Herded Gibbs is shown to outperform Gibbs in the tasks of image denoising with MRFs and named entity recognition with CRFs. However, the convergence for herded Gibbs for sparsely connected probabilistic graphical models is still an open problem.


Affinity Weighted Embedding

Supervised (linear) embedding models like Wsabie and PSI have proven successful at ranking, recommendation and annotation tasks. However, despite being scalable to large datasets they do not take full advantage of the extra data due to their linear nature, and typically underfit. We propose a new class of models which aim to provide improved performance while retaining many of the benefits of the existing class of embedding models. Our new approach works by iteratively learning a linear embedding model where the next iteration's features and labels are reweighted as a function of the previous iteration. We describe several variants of the family, and give some initial results.


Latent Relation Representations for Universal Schemas

Traditional relation extraction predicts relations within some fixed and finite target schema. Machine learning approaches to this task require either manual annotation or, in the case of distant supervision, existing structured sources of the same schema. The need for existing datasets can be avoided by using a universal schema: the union of all involved schemas (surface form predicates as in OpenIE, and relations in the schemas of pre-existing databases). This schema has an almost unlimited set of relations (due to surface forms), and supports integration with existing structured data (through the relation types of existing databases). To populate a database of such schema we present a family of matrix factorization models that predict affinity between database tuples and relations. We show that this achieves substantially higher accuracy than the traditional classification approach. More importantly, by operating simultaneously on relations observed in text and in pre-existing structured DBs such as Freebase, we are able to reason about unstructured and structured data in mutually-supporting ways. By doing so our approach outperforms state-of-the-art distant supervision systems.


A Linearly Convergent Conditional Gradient Algorithm with Applications to Online and Stochastic Optimization

Linear optimization is many times algorithmically simpler than non-linear convex optimization. Linear optimization over matroid polytopes, matching polytopes and path polytopes are example of problems for which we have simple and efficient combinatorial algorithms, but whose non-linear convex counterpart is harder and admits significantly less efficient algorithms. This motivates the computational model of convex optimization, including the offline, online and stochastic settings, using a linear optimization oracle. In this computational model we give several new results that improve over the previous state-of-the-art. Our main result is a novel conditional gradient algorithm for smooth and strongly convex optimization over polyhedral sets that performs only a single linear optimization step over the domain on each iteration and enjoys a linear convergence rate. This gives an exponential improvement in convergence rate over previous results. Based on this new conditional gradient algorithm we give the first algorithms for online convex optimization over polyhedral sets that perform only a single linear optimization step over the domain while having optimal regret guarantees, answering an open question of Kalai and Vempala, and Hazan and Kale. Our online algorithms also imply conditional gradient algorithms for non-smooth and stochastic convex optimization with the same convergence rates as projected (sub)gradient methods.


Cellular Tree Classifiers

The cellular tree classifier model addresses a fundamental problem in the design of classifiers for a parallel or distributed computing world: Given a data set, is it sufficient to apply a majority rule for classification, or shall one split the data into two or more parts and send each part to a potentially different computer (or cell) for further processing? At first sight, it seems impossible to define with this paradigm a consistent classifier as no cell knows the "original data size", $n$. However, we show that this is not so by exhibiting two different consistent classifiers. The consistency is universal but is only shown for distributions with nonatomic marginals.


Pattern Matching for Self- Tuning of MapReduce Jobs

In this paper, we study CPU utilization time patterns of several MapReduce applications. After extracting running patterns of several applications, they are saved in a reference database to be later used to tweak system parameters to efficiently execute unknown applications in future. To achieve this goal, CPU utilization patterns of new applications are compared with the already known ones in the reference database to find/predict their most probable execution patterns. Because of different patterns lengths, the Dynamic Time Warping (DTW) is utilized for such comparison; a correlation analysis is then applied to DTWs outcomes to produce feasible similarity patterns. Three real applications (WordCount, Exim Mainlog parsing and Terasort) are used to evaluate our hypothesis in tweaking system parameters in executing similar applications. Results were very promising and showed effectiveness of our approach on pseudo-distributed MapReduce platforms.


A Linear Time Active Learning Algorithm for Link Classification -- Full Version --

We present very efficient active learning algorithms for link classification in signed networks. Our algorithms are motivated by a stochastic model in which edge labels are obtained through perturbations of a initial sign assignment consistent with a two-clustering of the nodes. We provide a theoretical analysis within this model, showing that we can achieve an optimal (to whithin a constant factor) number of mistakes on any graph G = (V,E) such that |E| = \Omega(|V|^{3/2}) by querying O(|V|^{3/2}) edge labels. More generally, we show an algorithm that achieves optimality to within a factor of O(k) by querying at most order of |V| + (|V|/k)^{3/2} edge labels. The running time of this algorithm is at most of order |E| + |V|\log|V|.


A Correlation Clustering Approach to Link Classification in Signed Networks -- Full Version --

Motivated by social balance theory, we develop a theory of link classification in signed networks using the correlation clustering index as measure of label regularity. We derive learning bounds in terms of correlation clustering within three fundamental transductive learning settings: online, batch and active. Our main algorithmic contribution is in the active setting, where we introduce a new family of efficient link classifiers based on covering the input graph with small circuits. These are the first active algorithms for link classification with mistake bounds that hold for arbitrary signed networks.


Active Learning of Inverse Models with Intrinsically Motivated Goal Exploration in Robots

We introduce the Self-Adaptive Goal Generation - Robust Intelligent Adaptive Curiosity (SAGG-RIAC) architecture as an intrinsi- cally motivated goal exploration mechanism which allows active learning of inverse models in high-dimensional redundant robots. This allows a robot to efficiently and actively learn distributions of parameterized motor skills/policies that solve a corresponding distribution of parameterized tasks/goals. The architecture makes the robot sample actively novel parameterized tasks in the task space, based on a measure of competence progress, each of which triggers low-level goal-directed learning of the motor policy pa- rameters that allow to solve it. For both learning and generalization, the system leverages regression techniques which allow to infer the motor policy parameters corresponding to a given novel parameterized task, and based on the previously learnt correspondences between policy and task parameters. We present experiments with high-dimensional continuous sensorimotor spaces in three different robotic setups: 1) learning the inverse kinematics in a highly-redundant robotic arm, 2) learning omnidirectional locomotion with motor primitives in a quadruped robot, 3) an arm learning to control a fishing rod with a flexible wire. We show that 1) exploration in the task space can be a lot faster than exploration in the actuator space for learning inverse models in redundant robots; 2) selecting goals maximizing competence progress creates developmental trajectories driving the robot to progressively focus on tasks of increasing complexity and is statistically significantly more efficient than selecting tasks randomly, as well as more efficient than different standard active motor babbling methods; 3) this architecture allows the robot to actively discover which parts of its task space it can learn to reach and which part it cannot.


Dirichlet draws are sparse with high probability

This note provides an elementary proof of the folklore fact that draws from a Dirichlet distribution (with parameters less than 1) are typically sparse (most coordinates are small).


Evaluation of a Supervised Learning Approach for Stock Market Operations

Data mining methods have been widely applied in financial markets, with the purpose of providing suitable tools for prices forecasting and automatic trading. Particularly, learning methods aim to identify patterns in time series and, based on such patterns, to recommend buy/sell operations. The objective of this work is to evaluate the performance of Random Forests, a supervised learning method based on ensembles of decision trees, for decision support in stock markets. Preliminary results indicate good rates of successful operations and good rates of return per operation, providing a strong motivation for further research in this topic.


Heteroscedastic Conditional Ordinal Random Fields for Pain Intensity Estimation from Facial Images

We propose a novel method for automatic pain intensity estimation from facial images based on the framework of kernel Conditional Ordinal Random Fields (KCORF). We extend this framework to account for heteroscedasticity on the output labels(i.e., pain intensity scores) and introduce a novel dynamic features, dynamic ranks, that impose temporal ordinal constraints on the static ranks (i.e., intensity scores). Our experimental results show that the proposed approach outperforms state-of-the art methods for sequence classification with ordinal data and other ordinal regression models. The approach performs significantly better than other models in terms of Intra-Class Correlation measure, which is the most accepted evaluation measure in the tasks of facial behaviour intensity estimation.


Piecewise Linear Multilayer Perceptrons and Dropout

We propose a new type of hidden layer for a multilayer perceptron, and demonstrate that it obtains the best reported performance for an MLP on the MNIST dataset.


Active Learning on Trees and Graphs

We investigate the problem of active learning on a given tree whose nodes are assigned binary labels in an adversarial way. Inspired by recent results by Guillory and Bilmes, we characterize (up to constant factors) the optimal placement of queries so to minimize the mistakes made on the non-queried nodes. Our query selection algorithm is extremely efficient, and the optimal number of mistakes on the non-queried nodes is achieved by a simple and efficient mincut classifier. Through a simple modification of the query selection algorithm we also show optimality (up to constant factors) with respect to the trade-off between number of queries and number of mistakes on non-queried nodes. By using spanning trees, our algorithms can be efficiently applied to general graphs, although the problem of finding optimal and efficient active learning algorithms for general graphs remains open. Towards this end, we provide a lower bound on the number of mistakes made on arbitrary graphs by any active learning algorithm using a number of queries which is up to a constant fraction of the graph size.


See the Tree Through the Lines: The Shazoo Algorithm -- Full Version --

Predicting the nodes of a given graph is a fascinating theoretical problem with applications in several domains. Since graph sparsification via spanning trees retains enough information while making the task much easier, trees are an important special case of this problem. Although it is known how to predict the nodes of an unweighted tree in a nearly optimal way, in the weighted case a fully satisfactory algorithm is not available yet. We fill this hole and introduce an efficient node predictor, Shazoo, which is nearly optimal on any weighted tree. Moreover, we show that Shazoo can be viewed as a common nontrivial generalization of both previous approaches for unweighted trees and weighted lines. Experiments on real-world datasets confirm that Shazoo performs well in that it fully exploits the structure of the input tree, and gets very close to (and sometimes better than) less scalable energy minimization methods.


Properties of the Least Squares Temporal Difference learning algorithm

This paper presents four different ways of looking at the well-known Least Squares Temporal Differences (LSTD) algorithm for computing the value function of a Markov Reward Process, each of them leading to different insights: the operator-theory approach via the Galerkin method, the statistical approach via instrumental variables, the linear dynamical system view as well as the limit of the TD iteration. We also give a geometric view of the algorithm as an oblique projection. Furthermore, there is an extensive comparison of the optimization problem solved by LSTD as compared to Bellman Residual Minimization (BRM). We then review several schemes for the regularization of the LSTD solution. We then proceed to treat the modification of LSTD for the case of episodic Markov Reward Processes.


The connection between Bayesian estimation of a Gaussian random field and RKHS

Reconstruction of a function from noisy data is often formulated as a regularized optimization problem over an infinite-dimensional reproducing kernel Hilbert space (RKHS). The solution describes the observed data and has a small RKHS norm. When the data fit is measured using a quadratic loss, this estimator has a known statistical interpretation. Given the noisy measurements, the RKHS estimate represents the posterior mean (minimum variance estimate) of a Gaussian random field with covariance proportional to the kernel associated with the RKHS. In this paper, we provide a statistical interpretation when more general losses are used, such as absolute value, Vapnik or Huber. Specifically, for any finite set of sampling locations (including where the data were collected), the MAP estimate for the signal samples is given by the RKHS estimate evaluated at these locations.


Online Learning with Pairwise Loss Functions

Efficient online learning with pairwise loss functions is a crucial component in building large-scale learning system that maximizes the area under the Receiver Operator Characteristic (ROC) curve. In this paper we investigate the generalization performance of online learning algorithms with pairwise loss functions. We show that the existing proof techniques for generalization bounds of online algorithms with a univariate loss can not be directly applied to pairwise losses. In this paper, we derive the first result providing data-dependent bounds for the average risk of the sequence of hypotheses generated by an arbitrary online learner in terms of an easily computable statistic, and show how to extract a low risk hypothesis from the sequence. We demonstrate the generality of our results by applying it to two important problems in machine learning. First, we analyze two online algorithms for bipartite ranking; one being a natural extension of the perceptron algorithm and the other using online convex optimization. Secondly, we provide an analysis for the risk bound for an online algorithm for supervised metric learning.


Why Size Matters: Feature Coding as Nystrom Sampling

Recently, the computer vision and machine learning community has been in favor of feature extraction pipelines that rely on a coding step followed by a linear classifier, due to their overall simplicity, well understood properties of linear classifiers, and their computational efficiency. In this paper we propose a novel view of this pipeline based on kernel methods and Nystrom sampling. In particular, we focus on the coding of a data point with a local representation based on a dictionary with fewer elements than the number of data points, and view it as an approximation to the actual function that would compute pair-wise similarity to all data points (often too many to compute in practice), followed by a Nystrom sampling step to select a subset of all data points. Furthermore, since bounds are known on the approximation power of Nystrom sampling as a function of how many samples (i.e. dictionary size) we consider, we can derive bounds on the approximation of the exact (but expensive to compute) kernel matrix, and use it as a proxy to predict accuracy as a function of the dictionary size, which has been observed to increase but also to saturate as we increase its size. This model may help explaining the positive effect of the codebook size and justifying the need to stack more layers (often referred to as deep learning), as flat models empirically saturate as we add more complexity.


Multi-class Generalized Binary Search for Active Inverse Reinforcement Learning

This paper addresses the problem of learning a task from demonstration. We adopt the framework of inverse reinforcement learning, where tasks are represented in the form of a reward function. Our contribution is a novel active learning algorithm that enables the learning agent to query the expert for more informative demonstrations, thus leading to more sample-efficient learning. For this novel algorithm (Generalized Binary Search for Inverse Reinforcement Learning, or GBS-IRL), we provide a theoretical bound on sample complexity and illustrate its applicability on several different tasks. To our knowledge, GBS-IRL is the first active IRL algorithm with provable sample complexity bounds. We also discuss our method in light of other existing methods in the literature and its general applicability in multi-class classification problems. Finally, motivated by recent work on learning from demonstration in robots, we also discuss how different forms of human feedback can be integrated in a transparent manner in our learning framework.


Regularization and nonlinearities for neural language models: when are they needed?

Neural language models (LMs) based on recurrent neural networks (RNN) are some of the most successful word and character-level LMs. Why do they work so well, in particular better than linear neural LMs? Possible explanations are that RNNs have an implicitly better regularization or that RNNs have a higher capacity for storing patterns due to their nonlinearities or both. Here we argue for the first explanation in the limit of little training data and the second explanation for large amounts of text data. We show state-of-the-art performance on the popular and small Penn dataset when RNN LMs are regularized with random dropout. Nonetheless, we show even better performance from a simplified, much less expressive linear RNN model without off-diagonal entries in the recurrent matrix. We call this model an impulse-response LM (IRLM). Using random dropout, column normalization and annealed learning rates, IRLMs develop neurons that keep a memory of up to 50 words in the past and achieve a perplexity of 102.5 on the Penn dataset. On two large datasets however, the same regularization methods are unsuccessful for both models and the RNN's expressivity allows it to overtake the IRLM by 10 and 20 percent perplexity, respectively. Despite the perplexity gap, IRLMs still outperform RNNs on the Microsoft Research Sentence Completion (MRSC) task. We develop a slightly modified IRLM that separates long-context units (LCUs) from short-context units and show that the LCUs alone achieve a state-of-the-art performance on the MRSC task of 60.8%. Our analysis indicates that a fruitful direction of research for neural LMs lies in developing more accessible internal representations, and suggests an optimization regime of very high momentum terms for effectively training such models.


Transfer Topic Modeling with Ease and Scalability

The increasing volume of short texts generated on social media sites, such as Twitter or Facebook, creates a great demand for effective and efficient topic modeling approaches. While latent Dirichlet allocation (LDA) can be applied, it is not optimal due to its weakness in handling short texts with fast-changing topics and scalability concerns. In this paper, we propose a transfer learning approach that utilizes abundant labeled documents from other domains (such as Yahoo! News or Wikipedia) to improve topic modeling, with better model fitting and result interpretation. Specifically, we develop Transfer Hierarchical LDA (thLDA) model, which incorporates the label information from other domains via informative priors. In addition, we develop a parallel implementation of our model for large-scale applications. We demonstrate the effectiveness of our thLDA model on both a microblogging dataset and standard text collections including AP and RCV1 datasets.


Reinforcement learning from comparisons: Three alternatives is enough, two is not

The paper deals with the problem of finding the best alternatives on the basis of pairwise comparisons when these comparisons need not be transitive. In this setting, we study a reinforcement urn model. We prove convergence to the optimal solution when reinforcement of a winning alternative occurs each time after considering three random alternatives. The simpler process, which reinforces the winner of a random pair does not always converges: it may cycle.


Phase Diagram and Approximate Message Passing for Blind Calibration and Dictionary Learning

We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of phase transitions delimiting impossible, possible-but-hard and possible inference regions. We also introduce an approximate message passing algorithm that asymptotically matches the theoretical performance, and show through numerical tests that it performs very well, for the calibration problem, for tractable system sizes.


Recycling Proof Patterns in Coq: Case Studies

Development of Interactive Theorem Provers has led to the creation of big libraries and varied infrastructures for formal proofs. However, despite (or perhaps due to) their sophistication, the re-use of libraries by non-experts or across domains is a challenge. In this paper, we provide detailed case studies and evaluate the machine-learning tool ML4PG built to interactively data-mine the electronic libraries of proofs, and to provide user guidance on the basis of proof patterns found in the existing libraries.


Weighted Last-Step Min-Max Algorithm with Improved Sub-Logarithmic Regret

In online learning the performance of an algorithm is typically compared to the performance of a fixed function from some class, with a quantity called regret. Forster proposed a last-step min-max algorithm which was somewhat simpler than the algorithm of Vovk, yet with the same regret. In fact the algorithm he analyzed assumed that the choices of the adversary are bounded, yielding artificially only the two extreme cases. We fix this problem by weighing the examples in such a way that the min-max problem will be well defined, and provide analysis with logarithmic regret that may have better multiplicative factor than both bounds of Forster and Vovk. We also derive a new bound that may be sub-logarithmic, as a recent bound of Orabona et.al, but may have better multiplicative factor. Finally, we analyze the algorithm in a weak-type of non-stationary setting, and show a bound that is sub-linear if the non-stationarity is sub-linear as well.


Sample Complexity of Bayesian Optimal Dictionary Learning

We consider a learning problem of identifying a dictionary matrix D (M times N dimension) from a sample set of M dimensional vectors Y = N^{-1/2} DX, where X is a sparse matrix (N times P dimension) in which the density of non-zero entries is 0<rho< 1. In particular, we focus on the minimum sample size P_c (sample complexity) necessary for perfectly identifying D of the optimal learning scheme when D and X are independently generated from certain distributions. By using the replica method of statistical mechanics, we show that P_c=O(N) holds as long as alpha = M/N >rho is satisfied in the limit of N to infinity. Our analysis also implies that the posterior distribution given Y is condensed only at the correct dictionary D when the compression rate alpha is greater than a certain critical value alpha_M(rho). This suggests that belief propagation may allow us to learn D with a low computational complexity using O(N) samples.


LA-LDA: A Limited Attention Topic Model for Social Recommendation

Social media users have finite attention which limits the number of incoming messages from friends they can process. Moreover, they pay more attention to opinions and recommendations of some friends more than others. In this paper, we propose LA-LDA, a latent topic model which incorporates limited, non-uniformly divided attention in the diffusion process by which opinions and information spread on the social network. We show that our proposed model is able to learn more accurate user models from users' social network and item adoption behavior than models which do not take limited attention into account. We analyze voting on news items on the social news aggregator Digg and show that our proposed model is better able to predict held out votes than alternative models. Our study demonstrates that psycho-socially motivated models have better ability to describe and predict observed behavior than models which only consider topics.


Equitability Analysis of the Maximal Information Coefficient, with Comparisons

A measure of dependence is said to be equitable if it gives similar scores to equally noisy relationships of different types. Equitability is important in data exploration when the goal is to identify a relatively small set of strongest associations within a dataset as opposed to finding as many non-zero associations as possible, which often are too many to sift through. Thus an equitable statistic, such as the maximal information coefficient (MIC), can be useful for analyzing high-dimensional data sets. Here, we explore both equitability and the properties of MIC, and discuss several aspects of the theory and practice of MIC. We begin by presenting an intuition behind the equitability of MIC through the exploration of the maximization and normalization steps in its definition. We then examine the speed and optimality of the approximation algorithm used to compute MIC, and suggest some directions for improving both. Finally, we demonstrate in a range of noise models and sample sizes that MIC is more equitable than natural alternatives, such as mutual information estimation and distance correlation.


Hierarchical Data Representation Model - Multi-layer NMF

In this paper, we propose a data representation model that demonstrates hierarchical feature learning using nsNMF. We extend unit algorithm into several layers. Experiments with document and image data successfully discovered feature hierarchies. We also prove that proposed method results in much better classification and reconstruction performance, especially for small number of features. feature hierarchies.


An improvement to k-nearest neighbor classifier

K-Nearest neighbor classifier (k-NNC) is simple to use and has little design time like finding k values in k-nearest neighbor classifier, hence these are suitable to work with dynamically varying data-sets. There exists some fundamental improvements over the basic k-NNC, like weighted k-nearest neighbors classifier (where weights to nearest neighbors are given based on linear interpolation), using artificially generated training set called bootstrapped training set, etc. These improvements are orthogonal to space reduction and classification time reduction techniques, hence can be coupled with any of them. The paper proposes another improvement to the basic k-NNC where the weights to nearest neighbors are given based on Gaussian distribution (instead of linear interpolation as done in weighted k-NNC) which is also independent of any space reduction and classification time reduction technique. We formally show that our proposed method is closely related to non-parametric density estimation using a Gaussian kernel. We experimentally demonstrate using various standard data-sets that the proposed method is better than the existing ones in most cases.


Discriminative Feature Selection for Uncertain Graph Classification

Mining discriminative features for graph data has attracted much attention in recent years due to its important role in constructing graph classifiers, generating graph indices, etc. Most measurement of interestingness of discriminative subgraph features are defined on certain graphs, where the structure of graph objects are certain, and the binary edges within each graph represent the "presence" of linkages among the nodes. In many real-world applications, however, the linkage structure of the graphs is inherently uncertain. Therefore, existing measurements of interestingness based upon certain graphs are unable to capture the structural uncertainty in these applications effectively. In this paper, we study the problem of discriminative subgraph feature selection from uncertain graphs. This problem is challenging and different from conventional subgraph mining problems because both the structure of the graph objects and the discrimination score of each subgraph feature are uncertain. To address these challenges, we propose a novel discriminative subgraph feature selection method, DUG, which can find discriminative subgraph features in uncertain graphs based upon different statistical measures including expectation, median, mode and phi-probability. We first compute the probability distribution of the discrimination scores for each subgraph feature based on dynamic programming. Then a branch-and-bound algorithm is proposed to search for discriminative subgraphs efficiently. Extensive experiments on various neuroimaging applications (i.e., Alzheimer's Disease, ADHD and HIV) have been performed to analyze the gain in performance by taking into account structural uncertainties in identifying discriminative subgraph features for graph classification.


Political Disaffection: a case study on the Italian Twitter community

In our work we analyse the political disaffection or "the subjective feeling of powerlessness, cynicism, and lack of confidence in the political process, politicians, and democratic institutions, but with no questioning of the political regime" by exploiting Twitter data through machine learning techniques. In order to validate the quality of the time-series generated by the Twitter data, we highlight the relations of these data with political disaffection as measured by means of public opinion surveys. Moreover, we show that important political news of Italian newspapers are often correlated with the highest peaks of the produced time-series.


Clustering-Based Matrix Factorization

Recommender systems are emerging technologies that nowadays can be found in many applications such as Amazon, Netflix, and so on. These systems help users to find relevant information, recommendations, and their preferred items. Slightly improvement of the accuracy of these recommenders can highly affect the quality of recommendations. Matrix Factorization is a popular method in Recommendation Systems showing promising results in accuracy and complexity. In this paper we propose an extension of matrix factorization which adds general neighborhood information on the recommendation model. Users and items are clustered into different categories to see how these categories share preferences. We then employ these shared interests of categories in a fusion by Biased Matrix Factorization to achieve more accurate recommendations. This is a complement for the current neighborhood aware matrix factorization models which rely on using direct neighborhood information of users and items. The proposed model is tested on two well-known recommendation system datasets: Movielens100k and Netflix. Our experiment shows applying the general latent features of categories into factorized recommender models improves the accuracy of recommendations. The current neighborhood-aware models need a great number of neighbors to acheive good accuracies. To the best of our knowledge, the proposed model is better than or comparable with the current neighborhood-aware models when they consider fewer number of neighbors.


Inferring Parameters and Structure of Latent Variable Models by Variational Bayes

Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance, carrying out the Bayesian program of computing the full posterior distributions over the parameters remains a difficult problem. Moreover, learning the structure of models with latent variables, for which the Bayesian approach is crucial, is yet a harder problem. In this paper I present the Variational Bayes framework, which provides a solution to these problems. This approach approximates full posterior distributions over model parameters and structures, as well as latent variables, in an analytical manner without resorting to sampling methods. Unlike in the Laplace approximation, these posteriors are generally non-Gaussian and no Hessian needs to be computed. The resulting algorithm generalizes the standard Expectation Maximization algorithm, and its convergence is guaranteed. I demonstrate that this algorithm can be applied to a large class of models in several domains, including unsupervised clustering and blind source separation.


Relative Loss Bounds for On-line Density Estimation with the Exponential Family of Distributions

We consider on-line density estimation with a parameterized density from the exponential family. The on-line algorithm receives one example at a time and maintains a parameter that is essentially an average of the past examples. After receiving an example the algorithm incurs a loss which is the negative log-likelihood of the example w.r.t. the past parameter of the algorithm. An off-line algorithm can choose the best parameter based on all the examples. We prove bounds on the additional total loss of the on-line algorithm over the total loss of the off-line algorithm. These relative loss bounds hold for an arbitrary sequence of examples. The goal is to design algorithms with the best possible relative loss bounds. We use a certain divergence to derive and analyze the algorithms. This divergence is a relative entropy between two exponential distributions.