We examine the problem of generating state-space compressions of POMDPs in a way that minimally impacts decision quality. We analyze the impact of compressions ondecision quality, observing that compressions that allow accurate policy evaluation (prediction of expected future reward) will not affect decision quality. Wederive a set of sufficient conditions that ensure accurate prediction in this respect, illustrate interesting mathematical properties these confer on lossless linear compressions,and use these to derive an iterative procedure for finding good linear lossy compressions. We also elaborate on how structured representations of a POMDP can be used to find such compressions.

According to a series of influential models, dopamine (DA) neurons signal rewardprediction error using a temporal-difference (TD) algorithm. We address a problem not convincingly solved in these accounts: how to maintain a representation of cues that predict delayed consequences. Our new model uses a TD rule grounded in partially observable semi-Markov processes, a formalism that captures two largely neglected features of DA experiments: hidden state and temporal variability. Previous models predicted rewardsusing a tapped delay line representation of sensory inputs; we replace this with a more active process of inference about the underlying stateof the world. The DA system can then learn to map these inferred states to reward predictions using TD. The new model can explain previouslyvexing data on the responses of DA neurons in the face of temporal variability. By combining statistical model-based learning with a physiologically grounded TD theory, it also brings into contact with physiology some insights about behavior that had previously been confined to more abstract psychological models.

Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are intractable for large models. The intractability ofthese algorithms is due to a great extent to their generating an optimal policy over the entire belief space. However, in real POMDP problems most belief states are unlikely, and there is a structured, low-dimensional manifold of plausible beliefs embedded in the high-dimensional belief space. We introduce a new method for solving large-scale POMDPs by taking advantage of belief space sparsity. We reduce the dimensionality of the belief space by exponential family Principal Components Analysis [1], which allows us to turn the sparse, highdimensional beliefspace into a compact, low-dimensional representation in terms of learned features of the belief state. We then plan directly on the low-dimensional belief features. By planning in a low-dimensional space, we can find policies for POMDPs that are orders of magnitude larger than can be handled by conventional techniques. We demonstrate the use of this algorithm on a synthetic problem and also on a mobile robot navigation task.

Recently the Fisher score (or the Fisher kernel) is increasingly used as a feature extractor for classification problems. The Fisher score is a vector of parameter derivatives of loglikelihood of a probabilistic model. This paper gives a theoretical analysis about how class information is preserved inthe space of the Fisher score, which turns out that the Fisher score consists of a few important dimensions with class information and many nuisance dimensions. When we perform clustering with the Fisher score, K-Means type methods are obviously inappropriate because they make use of all dimensions. So we will develop a novel but simple clustering algorithmspecialized for the Fisher score, which can exploit important dimensions.This algorithm is successfully tested in experiments with artificial data and real data (amino acid sequences).

We study a new, model-free form of approximate policy iteration which uses Sarsa updates with linear state-action value function approximation for policy evaluation, and a "policy improvement operator" to generate a new policy based on the learned state-action values. We prove that if the policy improvement operator produces -soft policies and is Lipschitz continuous in the action values, with a constant that is not too large, then the approximate policy iteration algorithm converges to a unique solution fromany initial policy. To our knowledge, this is the first convergence resultfor any form of approximate policy iteration under similar computational-resource assumptions.

Multiagent learning is a key problem in AI. In the presence of multiple Nashequilibria, even agents with non-conflicting interests may not be able to learn an optimal coordination policy. The problem is exaccerbated ifthe agents do not know the game and independently receive noisy payoffs. So, multiagent reinforfcement learning involves two interrelated problems:identifying the game and learning to play.

We introduce a class of string kernels, called mismatch kernels, for use with support vector machines (SVMs) in a discriminative approach to the protein classification problem.

We describe a method for learning sparse multiscale image representations usinga sparse prior distribution over the basis function coefficients. The prior consists of a mixture of a Gaussian and a Dirac delta function, and thus encourages coefficients to have exact zero values. Coefficients for an image are computed by sampling from the resulting posterior distribution with a Gibbs sampler. The learned basis is similar to the Steerable Pyramid basis, and yields slightly higher SNR for the same number of active coefficients. Denoising usingthe learned image model is demonstrated for some standard test images, with results that compare favorably with other denoising methods.

Spontaneous facial expressions differ substantially from posed expressions, similar to how continuous, spontaneous speech differs from isolated words produced on command. Previous methods for automatic facial expression recognition assumed images were collected in controlled environments in which the subjects deliberately facedthe camera. Since people often nod or turn their heads, automatic recognition of spontaneous facial behavior requires methods for handling out-of-image-plane head rotations. Here we explore an approach basedon 3-D warping of images into canonical views. We evaluated the performance of the approach as a front-end for a spontaneous expression recognition system using support vector machines and hidden Markov models. This system employed general purpose learning mechanisms thatcan be applied to recognition of any facial movement. The system was tested for recognition of a set of facial actions defined by the Facial Action Coding System (FACS). We showed that 3D tracking and warping followed by machine learning techniques directly applied to the warped images, is a viable and promising technology for automatic facial expression recognition. One exciting aspect of the approach presented hereis that information about movement dynamics emerged out of filters which were derived from the statistics of images.

This paper presents a novel Hidden Markov Model architecture to model the joint probability of pairs of asynchronous sequences describing thesame event. It is based on two other Markovian models, namely Asynchronous Input/ Output Hidden Markov Models and Pair Hidden Markov Models. An EM algorithm to train the model is presented, as well as a Viterbi decoder that can be used to obtain theoptimal state sequence as well as the alignment between the two sequences. The model has been tested on an audiovisual speech recognition task using the M2VTS database and yielded robust performances under various noise conditions. 1 Introduction Hidden Markov Models (HMMs) are statistical tools that have been used successfully inthe last 30 years to model difficult tasks such as speech recognition [6) or biological sequence analysis [4). They are very well suited to handle discrete of continuous sequencesof varying sizes.