We describe the relationship between certain reinforcement learning (RL) methods based on dynamic programming (DP) and a class of unorthodox Monte Carlo methods for solving systems of linear equations proposed in the 1950's. These methods recast the solution of the linear system as the expected value of a statistic suitably defined over sample paths of a Markov chain. The significance of our observations lies in arguments (Curtiss, 1954) that these Monte Carlo methods scale better with respect to state-space size than do standard, iterative techniques for solving systems of linear equations. This analysis also establishes convergence rate estimates. Because methods used in RL systems for approximating the evaluation function of a fixed control policy also approximate solutions to systems of linear equations, the connection to these Monte Carlo methods establishes that algorithms very similar to TD algorithms (Sutton, 1988) are asymptotically more efficient in a precise sense than other methods for evaluating policies. Further, all DPbased RL methods have some of the properties of these Monte Carlo algorithms, that although RL is often perceived towhich suggests be slow, for sufficiently large problems, it may in fact be more efficient than other known classes of methods capable of producing the same results.

To assess the state of the art and identify issues requiring further investigation, a workshop on qualitative and abstract probability was held during the third week of November 1993. This workshop brought together a mix of active researchers from academia, industry, and government interested in the practical and theoretical impact of these abstractions on techniques, methods, and tools for solving complex AI tasks. The result was a set of specific recommendations on the most promising and important avenues for future research.

This paper is a multidisciplinary review of empirical, statistical learning from a graphical model perspective. Well-known examples of graphical models include Bayesian networks, directed graphs representing a Markov chain, and undirected networks representing a Markov field. These graphical models are extended to model data analysis and empirical learning using the notation of plates. Graphical operations for simplifying and manipulating a problem are provided including decomposition, differentiation, andthe manipulation of probability models from the exponential family. Two standard algorithm schemas for learning are reviewed in a graphical framework: Gibbs sampling and the expectation maximizationalgorithm. Using these operations and schemas, some popular algorithms can be synthesized from their graphical specification. This includes versions of linear regression, techniques for feed-forward networks, and learning Gaussian and discrete Bayesian networks from data. The paper concludes by sketching some implications for data analysis and summarizing how some popular algorithms fall within the framework presented. The main original contributions here are the decompositiontechniques and the demonstration that graphical models provide a framework for understanding and developing complex learning algorithms.

Several factors Chapter 2 describes a small fragment Chapters 8, 9, and 10 describe have led to the increase in interest in of probability and information recent research on more isolated this field, which is heavily influenced theory, including brief coverage of aspects of parsing and language analysis.

The attempt to find a single "optimal" weight vector in conventional network training can lead to overfitting and poor generalization. Bayesian methods avoid this, without the need for a validation set, by averaging the outputs of many networks with weights sampled from the posterior distribution given the training data. This sample can be obtained by simulating a stochastic dynamical system that has the posterior as its stationary distribution.

We present a methodological framework enabling a detailed description of the performance of Hopfield-like attractor neural networks (ANN) in the first two iterations. Using the Bayesian approach, we find that performance is improved when a history-based term is included in the neuron's dynamics. A further enhancement of the network's performance is achieved by judiciously choosing the censored neurons (those which become active in a given iteration) on the basis of the magnitude of their post-synaptic potentials. The contribution of biologically plausible, censored, historydependent dynamics is especially marked in conditions of low firing activity and sparse connectivity, two important characteristics of the mammalian cortex. In such networks, the performance attained is higher than the performance of two'independent' iterations, which represents an upper bound on the performance of history-independent networks.

We would like to incorporate speaker-dependent consistencies, such as gender, in an otherwise speaker-independent speech recognition system. In this paper we discuss a Gender Dependent Neural Network (GDNN) which can be tuned for each gender, while sharing most of the speaker independent parameters. We use a classification network to help generate gender-dependent phonetic probabilities for a statistical (HMM) recognition system. The gender classification net predicts the gender with high accuracy, 98.3% on a Resource Management test set. However, the integration of the GDNN into our hybrid HMM-neural network recognizer provided an improvement in the recognition score that is not statistically significant on a Resource Management test set.

We analyze the "query by committee" algorithm, a method for filtering informative queries from a random stream of inputs. We show that if the two-member committee algorithm achieves information gain with positive lower bound, then the prediction error decreases exponentially with the number of queries. We show that, in particular, this exponential decrease holds for query learning of thresholded smooth functions.

The classical computational model for stereo vision incorporates a uniqueness inhibition constraint to enforce a one-to-one feature match, thereby sacrificing the ability to handle transparency. Critics of the model disregard the uniqueness constraint and argue that the smoothness constraint can provide the excitation support required for transparency computation. However, this modification fails in neighborhoods with sparse features. We propose a Bayesian approach to stereo vision with priors favoring cohesive over transparent surfaces. The disparity and its segmentation into a multi-layer "depth planes" representation are simultaneously computed. The smoothness constraint propagates support within each layer, providing mutual excitation for non-neighboring transparent or partially occluded regions. Test results for various random-dot and other stereograms are presented.

University of Toronto University of Toronto University of Colorado Toronto, ONT M5S lA4 Toronto, ONT M5S lA4 Boulder, CO 80309-0430 Abstract We present a general formulation for a network of stochastic directional units. This formulation is an extension of the Boltzmann machine in which the units are not binary, but take on values in a cyclic range, between 0 and 271' radians. The conditional distribution of a unit's stochastic state is a circular version of the Gaussian probability distribution, known as the von Mises distribution. This combination of a value and a certainty provides additional representational power in a unit. Many kinds of information can naturally be represented in terms of angular, or directional, variables.