The problem of reinforcement learning in large factored Markov decision processes is explored. The Q-value of a state-action pair is approximated by the free energy of a product of experts network. Network parameters are learned online using a modified SARSA algorithm which minimizes the inconsistency of the Q-values of consecutive state-action pairs. Actions arechosen based on the current value estimates by fixing the current state and sampling actions from the network using Gibbs sampling. The algorithm is tested on a cooperative multi-agent task. The product of experts model is found to perform comparably to table-based Q-Iearning for small instances of the task, and continues to perform well when the problem becomes too large for a table-based representation.

We present a computational model of the neural mechanisms in the parietal andtemporal lobes that support spatial navigation, recall of scenes and imagery of the products of recall. Long term representations are stored in the hippocampus, and are associated with local spatial and object-related features in the parahippocampal region. Viewer-centered representations are dynamically generated from long term memory in the parietal part of the model. The model thereby simulates recall and imagery oflocations and objects in complex environments. After parietal damage, the model exhibits hemispatial neglect in mental imagery that rotates with the imagined perspective of the observer, as in the famous Milan Square experiment [1]. Our model makes novel predictions for the neural representations in the parahippocampal and parietal regions and for behavior in healthy volunteers and neuropsychological patients.

The product of experts learning procedure [1] can discover a set of stochastic binary features that constitute a nonlinear generative model of handwritten images of digits. The quality of generative models learned in this way can be assessed by learning a separate model for each class of digit and then comparing the unnormalized probabilities of test images under the 10 different class-specific models. To improve discriminative performance, it is helpful to learn a hierarchy of separate models for each digit class. Each model in the hierarchy has one layer of hidden units and the nth level model is trained on data that consists of the activities of the hidden units in the already trained (n - l)th level model. After training, eachlevel produces a separate, unnormalized log probabilty score. With a three-level hierarchy for each of the 10 digit classes, a test image produces 30 scores which can be used as inputs to a supervised, logistic classificationnetwork that is trained on separate data. On the MNIST database, our system is comparable with current state-of-the-art discriminative methods,demonstrating that the product of experts learning procedure can produce effective generative models of high-dimensional data. 1 Learning products of stochastic binary experts Hinton [1] describes a learning algorithm for probabilistic generative models that are composed ofa number of experts. Each expert specifies a probability distribution over the visible variables and the experts are combined by multiplying these distributions together and renormalizing.

When trying to recover 3D structure from a set of images, the most difficult problem is establishing the correspondence between the measurements. Most existing approaches assume that features can be tracked across frames, whereas methods that exploit rigidity constraints to facilitate matching do so only under restricted camera motion.In this paper we propose a Bayesian approach that avoids the brittleness associated with singling out one "best" correspondence, andinstead consider the distribution over all possible correspondences. We treat both a fully Bayesian approach that yields a posterior distribution, and a MAP approach that makes use of EM to maximize this posterior. We show how Markov chain Monte Carlo methods can be used to implement these techniques in practice, and present experimental results on real data.

A system has been developed to extract diagnostic information from jet engine carcass vibration data. Support Vector Machines applied to novelty detectionprovide a measure of how unusual the shape of a vibration signatureis, by learning a representation of normality. We describe a novel method for Support Vector Machines of including information from a second class for novelty detection and give results from the application toJet Engine vibration analysis.

We estimate a statistical model of typical activities from a large set of 3D periodic human motion data by segmenting these data automatically into "cycles". Then the mean and the principal componentsof the cycles are computed using a new algorithm that accounts for missing information and enforces smooth transitions betweencycles. The learned temporal model provides a prior probability distribution over human motions that can be used in a Bayesian framework for tracking human subjects in complex monocular video sequences and recovering their 3D motion. 1 Introduction The modeling and tracking of human motion in video is important for problems as varied as animation, video database search, sports medicine, and human-computer interaction. Technically, the human body can be approximated by a collection of articulated limbs and its motion can be thought of as a collection of time-series describing the joint angles as they evolve over time. A key challenge in modeling these joint angles involves decomposing the time-series into suitable temporal primitives.

We investigate a new kernel-based classifier: the Kernel Fisher Discriminant (KFD).A mathematical programming formulation based on the observation thatKFD maximizes the average margin permits an interesting modification of the original KFD algorithm yielding the sparse KFD. We find that both, KFD and the proposed sparse KFD, can be understood in an unifying probabilistic context. Furthermore, we show connections to Support Vector Machines and Relevance Vector Machines. From this understanding, we are able to outline an interesting kernel-regression technique based upon the KFD algorithm.

The concept of averaging over classifiers is fundamental to the Bayesian analysis of learning. Based on this viewpoint, it has recently beendemonstrated for linear classifiers that the centre of mass of version space (the set of all classifiers consistent with the training set) - also known as the Bayes point - exhibits excellent generalisationabilities. In this paper we present a method based on the simple perceptron learning algorithm which allows to overcome this algorithmic drawback. The method is algorithmically simpleand is easily extended to the multi-class case. We present experimental results on the MNIST data set of handwritten digitswhich show that Bayes point machines (BPMs) are competitive with the current world champion, the support vector machine.

These methods are compared on their performance on a visual speech recognition task. While the representations developed are specific to visual speech recognition, the methods themselvesare general purpose and applicable to other tasks. Our focus is on low-level data-driven methods based on the statistical properties of relatively untouched images, as opposed to approaches that work with contours or highly processed versions of the image. Padgett [8] and Bartlett [1] systematically studied statistical methods for developing representations on expression recognition tasks. They found that local wavelet-like representations consistently outperformed global representations, like eigenfaces. In this paper we also compare local versus global representations.

A stable learner is one for which the learned solution does not change much with small changes in the training set. The bounds we obtain do not depend on any measure of the complexity of the hypothesis space (e.g. VC dimension) but rather depend on how the learning algorithm searches this space, and can thus be applied even when the VC dimension is infinite. We demonstrate that regularization networks possess the required stability property and apply our method to obtain new bounds on their generalization performance.