The recent advances in computer speed and algorithms for probabilistic inference have led to a resurgence of work on planning under uncertainty. The aim is to design AI planners for environments where there might be incomplete or faulty information, where actions might not always have the same results, and where there might be trade-offs between the different possible outcomes of a plan. Addressing uncertainty in AI, planning algorithms will greatly increase the range of potential applications, but there is plenty of work to be done before we see practical decision-theoretic planning systems. This article outlines some of the challenges that need to be overcome and surveys some of the recent work in the area.

This article provides an overview of the field of qualitative decision theory: its motivating tasks and issues, its antecedents, and its prospects. Qualitative decision theory studies qualitative approaches to problems of decision making and their sound and effective reconciliation and integration with quantitative approaches. Although it inherits from a long tradition, the field offers a new focus on a number of important unanswered questions of common concern to AI, economics, law, psychology, and management.

A Bayesian network is a compact, expressive representation of uncertain relationships among parameters in a domain. In this article, I introduce basic methods for computing with Bayesian networks, starting with the simple idea of summing the probabilities of events of interest. The article introduces major current methods for exact computation, briefly surveys approximation methods, and closes with a brief discussion of open issues.

The last few years have seen a surge in interest in the use of techniques from Bayesian decision theory to address problems in AI. Decision theory provides a normative framework for representing and reasoning about decision problems under uncertainty. Within the context of this framework, researchers in uncertainty in the AI community have been developing computational techniques for building rational agents and representations suited to engineering their knowledge bases. This special issue reviews recent research in Bayesian problem-solving techniques. The articles cover the topics of inference in Bayesian networks, decision-theoretic planning, and qualitative decision theory. Here, I provide a brief introduction to Bayesian networks and then cover applications of Bayesian problem-solving techniques, knowledge-based model construction and structured representations, and the learning of graphic probability models.

We describe a variational approximation method for efficient inference in large-scale probabilistic models. Variational methods are deterministic procedures that provide approximations to marginal and conditional probabilities of interest. They provide alternatives to approximate inference methods based on stochastic sampling or search. We describe a variational approach to the problem of diagnostic inference in the `Quick Medical Reference' (QMR) network. The QMR network is a large-scale probabilistic graphical model built on statistical and expert knowledge. Exact probabilistic inference is infeasible in this model for all but a small set of cases. We evaluate our variational inference algorithm on a large set of diagnostic test cases, comparing the algorithm to a state-of-the-art stochastic sampling method.

The relationship between the Bayesian approach and the minimum description length approach is established. We sharpen and clarify the general modeling principles MDL and MML, abstracted as the ideal MDL principle and defined from Bayes's rule by means of Kolmogorov complexity. The basic condition under which the ideal principle should be applied is encapsulated as the Fundamental Inequality, which in broad terms states that the principle is valid when the data are random, relative to every contemplated hypothesis and also these hypotheses are random relative to the (universal) prior. Basically, the ideal principle states that the prior probability associated with the hypothesis should be given by the algorithmic universal probability, and the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized. If we restrict the model class to the finite sets then application of the ideal principle turns into Kolmogorov's minimal sufficient statistic. In general we show that data compression is almost always the best strategy, both in hypothesis identification and prediction.

This paper introduces a probability model, the mixture of trees that can account for sparse, dynamically changing dependence relationships. We present a family of efficient algorithms that use EM and the Minimum Spanning Tree algorithm to find the ML and MAP mixture of trees for a variety of priors, including the Dirichlet and the MDL priors.

This paper reports about an application of Bayes' inferred neural network classifiers in the field of automatic sleep staging. The reason for using Bayesian learning for this task is twofold. First, Bayesian inference is known to embody regularization automatically. Second, a side effect of Bayesian learning leads to larger variance of network outputs in regions without training data. This results in well known moderation effects, which can be used to detect outliers. In a 5 fold cross-validation experiment the full Bayesian solution found with R. Neals hybrid Monte Carlo algorithm, was not better than a single maximum a-posteriori (MAP) solution found with D.J. MacKay's evidence approximation. In a second experiment we studied the properties of both solutions in rejecting classification of movement artefacts.

In this paper, we discuss regularisation in online/sequential learning algorithms. In environments where data arrives sequentially, techniques such as cross-validation to achieve regularisation or model selection are not possible. Further, bootstrapping to determine a confidence level is not practical. To surmount these problems, a minimum variance estimation approach that makes use of the extended Kalman algorithm for training multi-layer perceptrons is employed. The novel contribution of this paper is to show the theoretical links between extended Kalman filtering, Sutton's variable learning rate algorithms and Mackay's Bayesian estimation framework. In doing so, we propose algorithms to overcome the need for heuristic choices of the initial conditions and noise covariance matrices in the Kalman approach.

Department of Cognitive Science Department of Cognitive Science University of California, San Diego University of California, San Diego La Jolla, CA 92092-0515 La Jolla, CA 92092-0515 Abstract We discuss the problem of catastrophic fusion in multimodal recognition systems. This problem arises in systems that need to fuse different channels in non-stationary environments. Practice shows that when recognition modules within each modality are tested in contexts inconsistent with their assumptions, their influence on the fused product tends to increase, with catastrophic results. We explore a principled solution to this problem based upon Bayesian ideas of competitive models and inference robustification: each sensory channel is provided with simple white-noise context models, and the perceptual hypothesis and context are jointly estimated. Consequently, context deviations are interpreted as changes in white noise contamination strength, automatically adjusting the influence of the module.