In this paper, we introduce REMAP, an approach for the training and estimation of posterior probabilities using a recursive algorithm that is reminiscent of the EMbased Forward-Backward (Liporace 1982) algorithm for the estimation of sequence likelihoods. Although verygeneral, the method is developed in the context of a statistical model for transition-based speech recognition using Artificial NeuralNetworks (ANN) to generate probabilities for Hidden Markov Models (HMMs). In the new approach, we use local conditional posterior probabilities of transitions to estimate global posterior probabilities of word sequences. Although we still use ANNs to estimate posterior probabilities, the network is trained with targets that are themselves estimates of local posterior probabilities. Aninitial experimental result shows a significant decrease in error-rate in comparison to a baseline system. 1 INTRODUCTION The ultimate goal in speech recognition is to determine the sequence of words that has been uttered.

We develop a refined mean field approximation for inference and learning in probabilistic neural networks. Our mean field theory, unlike most, does not assume that the units behave as independent degrees of freedom; instead, it exploits in a principled way the existence of large substructures that are computationally tractable. To illustrate the advantages of this framework, we show how to incorporate weak higher order interactions into a first-order hidden Markov model, treating the corrections (but not the first order structure) within mean field theory. 1 INTRODUCTION Learning the parameters in a probabilistic neural network may be viewed as a problem in statistical estimation.

Reinforcement learning has become one of the most actively studied learning frameworks in the area of intelligent autonomous agents. This article describes the results of a three-day meeting of leading researchers in this area that was sponsored by the National Science Foundation. Because reinforcement learning is an interdisciplinary topic, the workshop brought together researchers from a variety of fields, including machine learning, neural networks, AI, robotics, and operations research. Thirty leading researchers from the United States, Canada, Europe, and Japan, representing from many different universities, government, and industrial research laboratories participated in the workshop. The goals of the meeting were to (1) understand limitations of current reinforcement-learning systems and define promising directions for further research; (2) clarify the relationships between reinforcement learning and existing work in engineering fields, such as operations research; and (3) identify potential industrial applications of reinforcement learning.

A new method is proposed for exploiting causal independencies in exact Bayesian network inference. A Bayesian network can be viewed as representing a factorization of a joint probability into the multiplication of a set of conditional probabilities. We present a notion of causal independence that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability. The new formulation of causal independence lets us specify the conditional probability of a variable given its parents in terms of an associative and commutative operator, such as ``or'', ``sum'' or ``max'', on the contribution of each parent. We start with a simple algorithm VE for Bayesian network inference that, given evidence and a query variable, uses the factorization to find the posterior distribution of the query. We show how this algorithm can be extended to exploit causal independence. Empirical studies, based on the CPCS networks for medical diagnosis, show that this method is more efficient than previous methods and allows for inference in larger networks than previous algorithms.

Data mining and knowledge discovery in databases have been attracting a significant amount of research, industry, and media attention of late. What is all the excitement about? This article provides an overview of this emerging field, clarifying how data mining and knowledge discovery in databases are related both to each other and to related fields, such as machine learning, statistics, and databases. The article mentions particular real-world applications, specific data-mining techniques, challenges involved in real-world applications of knowledge discovery, and current and future research directions in the field.

We develop a mean field theory for sigmoid belief networks based on ideas from statistical mechanics. Our mean field theory provides a tractable approximation to the true probability distribution in these networks; it also yields a lower bound on the likelihood of evidence. We demonstrate the utility of this framework on a benchmark problem in statistical pattern recognition---the classification of handwritten digits.

Traditional databases commonly support efficient query and update procedures that operate in time which is sublinear in the size of the database. Our goal in this paper is to take a first step toward dynamic reasoning in probabilistic databases with comparable efficiency. We propose a dynamic data structure that supports efficient algorithms for updating and querying singly connected Bayesian networks. In the conventional algorithm, new evidence is absorbed in O(1) time and queries are processed in time O(N), where N is the size of the network. We propose an algorithm which, after a preprocessing phase, allows us to answer queries in time O(log N) at the expense of O(log N) time per evidence absorption. The usefulness of sub-linear processing time manifests itself in applications requiring (near) real-time response over large probabilistic databases. We briefly discuss a potential application of dynamic probabilistic reasoning in computational biology.

If data collection is costly, there is much to be gained by actively selecting particularly informative data points in a sequential way. In a Bayesian decision-theoretic framework we develop a query selection criterion which explicitly takes into account the intended use of the model predictions. By Markov Chain Monte Carlo methods the necessary quantities can be approximated to a desired precision. As the number of data points grows, the model complexity is modified by a Bayesian model selection strategy. The properties of two versions of the criterion ate demonstrated in numerical experiments.

Statistical models of discrete time series have a wide range of applications, most notably to problems in speech recognition (Juang & Rabiner, 1991) and molecular biology (Baldi, Chauvin, Hunkapiller, & McClure, 1992). A common problem in these fields is to find a probabilistic model, and a set of model parameters, that 436 Lawrence K. Saul, Michael I. Jordan

Multi-class classification problems can be efficiently solved by partitioning the original problem into sub-problems involving only two classes: for each pair of classes, a (potentially small) neural network is trained using only the data of these two classes. We show how to combine the outputs of the two-class neural networks in order to obtain posterior probabilities for the class decisions. The resulting probabilistic pairwise classifier is part of a handwriting recognition system which is currently applied to check reading. We present results on real world data bases and show that, from a practical point of view, these results compare favorably to other neural network approaches.