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.

A semi-supervised multitask learning (MTL) framework is presented, in which M parameterized semi-supervised classifiers, each associated with one of M partially labeled data manifolds, are learned jointly under the constraint of a softsharing prior imposed over the parameters of the classifiers. The unlabeled data are utilized by basing classifier learning on neighborhoods, induced by a Markov random walk over a graph representation of each manifold. Experimental results on real data sets demonstrate that semi-supervised MTL yields significant improvements in generalization performance over either semi-supervised single-task learning (STL) or supervised MTL.

Brain-Computer Interfaces can suffer from a large variance of the subject conditions within and across sessions. For example vigilance fluctuations in the individual, variable task involvement, workload etc. alter the characteristics of EEG signals and thus challenge a stable BCI operation. In the present work we aim to define features based on a variant of the common spatial patterns (CSP) algorithm that are constructed invariant with respect to such nonstationarities. We enforce invariance properties by adding terms to the denominator of a Rayleigh coefficient representation of CSP such as disturbance covariance matrices from fluctuations in visual processing. In this manner physiological prior knowledge can be used to shape the classification engine for BCI. As a proof of concept we present a BCI classifier that is robust to changes in the level of parietal α -activity. In other words, the EEG decoding still works when there are lapses in vigilance.

Many formal models of cognition implicitly use subjective probability distributions to capture the assumptions of human learners. Most applications of these models determine these distributions indirectly. We propose a method for directly determining the assumptions of human learners by sampling from subjective probability distributions. Using a correspondence between a model of human choice and Markov chain Monte Carlo (MCMC), we describe a method for sampling from the distributions over objects that people associate with different categories. In our task, subjects choose whether to accept or reject a proposed change to an object. The task is constructed so that these decisions follow an MCMC acceptance rule, defining a Markov chain for which the stationary distribution is the category distribution. We test this procedure for both artificial categories acquired in the laboratory, and natural categories acquired from experience.

We present a simple new criterion for classification, based on principles from lossy data compression. The criterion assigns a test sample to the class that uses the minimum number of additional bits to code the test sample, subject to an allowable distortion. We prove asymptotic optimality of this criterion for Gaussian data and analyze its relationships to classical classifiers. Theoretical results provide new insights into relationships among popular classifiers such as MAP and RDA, as well as unsupervised clustering methods based on lossy compression [13]. Minimizing the lossy coding length induces a regularization effect which stabilizes the (implicit) density estimate in a small-sample setting. Compression also provides a uniform means of handling classes of varying dimension. This simple classification criterion and its kernel and local versions perform competitively against existing classifiers on both synthetic examples and real imagery data such as handwritten digits and human faces, without requiring domain-specific information.

The present work aims to model the correspondence between facial motion and speech. The face and sound are modelled separately, with phonemes being the link between both. We propose a sequential model and evaluate its suitability for the generation of the facial animation from a sequence of phonemes, which we obtain from speech. We evaluate the results both by computing the error between generated sequences and real video, as well as with a rigorous double-blind test with human subjects. Experiments show that our model compares favourably to other existing methods and that the sequences generated are comparable to real video sequences.

We present an efficient generalization of the sparse pseudo-input Gaussian process (SPGP) model developed by Snelson and Ghahramani [1], applying it to binary classification problems.

Maximum variance unfolding (MVU) is an effective heuristic for dimensionality reduction. It produces a low-dimensional representation of the data by maximizing the variance of their embeddings while preserving the local distances of the original data. We show that MVU also optimizes a statistical dependence measure which aims to retain the identity of individual observations under the distancepreserving constraints. This general view allows us to design "colored" variants of MVU, which produce low-dimensional representations for a given task, e.g.