We first show how to represent sharp posterior probability distribu(cid:173) tions using real valued coefficients on broadly-tuned basis functions. Then we show how the precise times of spikes can be used to con(cid:173) vey the real-valued coefficients on the basis functions quickly and accurately. Finally we describe a simple simulation in which spik(cid:173) ing neurons learn to model an image sequence by fitting a dynamic generative model. A perceived object is represented in the brain by the activities of many neurons, but there is no general consensus on how the activities of individual neurons combine to represent the multiple properties of an object. We start by focussing on the case of a single object that has multiple instantiation parameters such as position, velocity, size and orientation. We assume that each neuron has an ideal stimulus in the space of instantiation parameters and that its activation rate or probability of activation falls off monotonically in all directions as the actual stimulus departs from this ideal.

We propose a new approach to the problem of searching a space of stochastic controllers for a Markov decision process (MDP) or a partially observable Markov decision process (POMDP). Following several other authors, our approach is based on searching in parameterized families of policies (for example, via gradient descent) to optimize solution qual(cid:173) ity. However, rather than trying to estimate the values and derivatives of a policy directly, we do so indirectly using estimates for the proba(cid:173) bility densities that the policy induces on states at the different points in time. This enables our algorithms to exploit the many techniques for efficient and robust approximate density propagation in stochastic sys(cid:173) tems. We show how our techniques can be applied both to deterministic propagation schemes (where the MDP's dynamics are given explicitly in compact form,) and to stochastic propagation schemes (where we have access only to a generative model, or simulator, of the MDP).

We present a Hidden Markov Model (HMM) for inferring the hidden psychological state (or neural activity) during single trial tMRI activa(cid:173) tion experiments with blocked task paradigms. Inference is based on Bayesian methodology, using a combination of analytical and a variety of Markov Chain Monte Carlo (MCMC) sampling techniques. The ad(cid:173) vantage of this method is that detection of short time learning effects be(cid:173) tween repeated trials is possible since inference is based only on single trial experiments.

We consider the problem of reliably choosing a near-best strategy from a restricted class of strategies TI in a partially observable Markov deci(cid:173) sion process (POMDP). We assume we are given the ability to simulate the POMDP, and study what might be called the sample complexity - that is, the amount of data one must generate in the POMDP in order to choose a good strategy. We prove upper bounds on the sample com(cid:173) plexity showing that, even for infinitely large and arbitrarily complex POMDPs, the amount of data needed can be finite, and depends only linearly on the complexity of the restricted strategy class TI, and expo(cid:173) nentially on the horizon time. This latter dependence can be eased in a variety of ways, including the application of gradient and local search algorithms.

We formulate a model for probability distributions on image spaces. We show that any distribution of images can be factored exactly into condi(cid:173) tional distributions of feature vectors at one resolution (pyramid level) conditioned on the image information at lower resolutions. We would like to factor this over positions in the pyramid levels to make it tractable, but such factoring may miss long-range dependencies. To fix this, we in(cid:173) troduce hidden class labels at each pixel in the pyramid. The result is a hierarchical mixture of conditional probabilities, similar to a hidden Markov model on a tree.

We present a Monte Carlo algorithm for learning to act in partially observable Markov decision processes (POMDPs) with real-valued state and action spaces. Our approach uses importance sampling for representing beliefs, and Monte Carlo approximation for belief propagation. A reinforcement learning algorithm, value iteration, is employed to learn value functions over belief states. Finally, a sample(cid:173) based version of nearest neighbor is used to generalize across states. Initial empirical results suggest that our approach works well in practical applications.

The problem of reinforcement learning in a non-Markov environment is explored using a dynamic Bayesian network, where conditional indepen(cid:173) dence assumptions between random variables are compactly represented by network parameters. The parameters are learned on-line, and approx(cid:173) imations are used to perform inference and to compute the optimal value function. The relative effects of inference and value function approxi(cid:173) mations on the quality of the final policy are investigated, by learning to solve a moderately difficult driving task. The two value function approx(cid:173) imations, linear and quadratic, were found to perform similarly, but the quadratic model was more sensitive to initialization. Both performed be(cid:173) low the level of human performance on the task.

The problem of developing good policies for partially observable Markov decision problems (POMDPs) remains one of the most challenging ar(cid:173) eas of research in stochastic planning. One line of research in this area involves the use of reinforcement learning with belief states, probabil(cid:173) ity distributions over the underlying model states. This is a promis(cid:173) ing method for small problems, but its application is limited by the in(cid:173) tractability of computing or representing a full belief state for large prob(cid:173) lems. Recent work shows that, in many settings, we can maintain an approximate belief state, which is fairly close to the true belief state. In particular, great success has been shown with approximate belief states that marginalize out correlations between state variables.

A new form of covariance modelling for Gaussian mixture models and hidden Markov models is presented. This is an extension to an efficient form of covariance modelling used in speech recognition, semi-tied co(cid:173) variance matrices. In the standard form of semi-tied covariance matrices the covariance matrix is decomposed into a highly shared decorrelating transform and a component-specific diagonal covariance matrix. The use of a factored decorrelating transform is presented in this paper. This fac(cid:173) toring effectively increases the number of possible transforms without in(cid:173) creasing the number of free parameters.

This paper explores a framework for recognition of image sequences using partially observable stochastic differential equation (SDE) models. Monte-Carlo importance sampling techniques are used for efficient estimation of sequence likelihoods and sequence likelihood gradients. Once the network dynamics are learned, we apply the SDE models to sequence recognition tasks in a manner similar to the way Hidden Markov models (HMMs) are commonly applied. The potential advantage of SDEs over HMMS is the use of contin(cid:173) uous state dynamics. We present encouraging results for a video sequence recognition task in which SDE models provided excellent performance when compared to hidden Markov models.