We unify f-divergences, Bregman divergences, surrogate loss bounds (regret bounds), proper scoring rules, matching losses, cost curves, ROC-curves and information. We do this by systematically studying integral and variational representations of these objects and in so doing identify their primitives which all are related to cost-sensitive binary classification. As well as clarifying relationships between generative and discriminative views of learning, the new machinery leads to tight and more general surrogate loss bounds and generalised Pinsker inequalities relating f-divergences to variational divergence. The new viewpoint illuminates existing algorithms: it provides a new derivation of Support Vector Machines in terms of divergences and relates Maximum Mean Discrepancy to Fisher Linear Discriminants. It also suggests new techniques for estimating f-divergences.

In bioinformatics it is often desirable to combine data from various measurement sources and thus structured feature vectors are to be analyzed that possess different intrinsic blocking characteristics (e.g., different patterns of missing values, observation noise levels, effective intrinsic dimensionalities). We propose a new machine learning tool, heterogeneous component analysis (HCA), for feature extraction in order to better understand the factors that underlie such complex structured heterogeneous data. HCA is a linear block-wise sparse Bayesian PCA based not only on a probabilistic model with block-wise residual variance terms but also on a Bayesian treatment of a block-wise sparse factor-loading matrix. We study various algorithms that implement our HCA concept extracting sparse heterogeneous structure by obtaining common components for the blocks and specific components within each block. Simulations on toy and bioinformatics data underline the usefulness of the proposed structured matrix factorization concept.

Semi-supervised inductive learning concerns how to learn a decision rule from a data set containing both labeled and unlabeled data. Several boosting algorithms have been extended to semi-supervised learning with various strategies. To our knowledge, however, none of them takes local smoothness constraints among data into account during ensemble learning. In this paper, we introduce a local smoothness regularizer to semi-supervised boosting algorithms based on the universal optimization framework of margin cost functionals. Our regularizer is applicable to existing semi-supervised boosting algorithms to improve their generalization and speed up their training. Comparative results on synthetic, benchmark and real world tasks demonstrate the effectiveness of our local smoothness regularizer. We discuss relevant issues and relate our regularizer to previous work.

We address the problem of factorial learning which associates a set of latent causes or features with the observed data. Factorial models usually assume that each feature has a single occurrence in a given data point. However, there are data such as images where latent features have multiple occurrences, e.g. a visual object class can have multiple instances shown in the same image. To deal with such cases, we present a probability model over non-negative integer valued matrices with possibly unbounded number of columns. This model can play the role of the prior in an nonparametric Bayesian learning scenario where both the latent features and the number of their occurrences are unknown. We use this prior together with a likelihood model for unsupervised learning from images using a Markov Chain Monte Carlo inference algorithm.

We propose a Bayesian undirected graphical model for co-training, or more generally for semi-supervised multi-view learning. This makes explicit the previously unstated assumptions of a large class of co-training type algorithms, and also clarifies the circumstances under which these assumptions fail. Building upon new insights from this model, we propose an improved method for co-training, which is a novel co-training kernel for Gaussian process classifiers. The resulting approach is convex and avoids local-maxima problems, unlike some previous multi-view learning methods. Furthermore, it can automatically estimate how much each view should be trusted, and thus accommodate noisy or unreliable views. Experiments on toy data and real world data sets illustrate the benefits of this approach.

Estimation of three-dimensional articulated human pose and motion from images is a central problem in computer vision. Much of the previous work has been limited by the use of crude generative models of humans represented as articulated collections of simple parts such as cylinders. Automatic initialization of such models has proved difficult and most approaches assume that the size and shape of the body parts are known a priori. In this paper we propose a method for automatically recovering a detailed parametric model of nonrigid body shape and pose from monocular imagery. Specifically, we represent the body using a param-eterized triangulated mesh model that is learned from a database of human range scans. We demonstrate a discriminative method to directly recover the model parameters from monocular images using a conditional mixture of kernel regressors. This predicted pose and shape are used to initialize a generative model for more detailed pose and shape estimation. The resulting approach allows fully automatic pose and shape recovery from monocular and multi-camera imagery. Experimental results show that our method is capable of robustly recovering articulated pose, shape and biometric measurements (e.g.

We propose a new measure of conditional dependence of random variables, based on normalized cross-covariance operators on reproducing kernel Hilbert spaces. Unlike previous kernel dependence measures, the proposed criterion does not depend on the choice of kernel in the limit of infinite data, for a wide class of kernels. At the same time, it has a straightforward empirical estimate with good convergence behaviour. We discuss the theoretical properties of the measure, and demonstrate its application in experiments.

We present four new reinforcement learning algorithms based on actor-critic and natural-gradient ideas, and provide their convergence proofs. Actor-critic reinforcement learning methods are online approximations to policy iteration in which the value-function parameters are estimated using temporal difference learning and the policy parameters are updated by stochastic gradient descent. Methods based on policy gradients in this way are of special interest because of their compatibility with function approximation methods, which are needed to handle large or infinite state spaces. The use of temporal difference learning in this way is of interest because in many applications it dramatically reduces the variance of the gradient estimates. The use of the natural gradient is of interest because it can produce better conditioned parameterizations and has been shown to further reduce variance in some cases. Our results extend prior two-timescale convergence results for actor-critic methods by Konda and Tsitsiklis by using temporal difference learning in the actor and by incorporating natural gradients, and they extend prior empirical studies of natural actor-critic methods by Peters, Vijayakumar and Schaal by providing the first convergence proofs and the first fully incremental algorithms.

Hierarchical penalization is a generic framework for incorporating prior information in the fitting of statistical models, when the explicative variables are organized in a hierarchical structure. The penalizer is a convex functional that performs soft selection at the group level, and shrinks variables within each group. This favors solutions with few leading terms in the final combination. The framework, originally derived for taking prior knowledge into account, is shown to be useful in linear regression, when several parameters are used to model the influence of one feature, or in kernel regression, for learning multiple kernels. Keywords - Optimization: constrained and convex optimization.

Semi-supervised learning, i.e. learning from both labeled and unlabeled data has received significant attention in the machine learning literature in recent years. Still our understanding of the theoretical foundations of the usefulness of unlabeled data remains somewhat limited. The simplest and the best understood situation is when the data is described by an identifiable mixture model, and where each class comes from a pure component. This natural setup and its implications ware analyzed in [11, 5]. One important result was that in certain regimes, labeled data becomes exponentially more valuable than unlabeled data. However, in most realistic situations, one would not expect that the data comes from a parametric mixture distribution with identifiable components.