Bruno Caprile I.R.S.T. Povo, Italy, 38050 Learning an input-output mapping from a set of examples can be regarded as synthesizing an approximation of a multidimensional function.

Function approximation on high-dimensional spaces is often thwarted by a lack of sufficient data to adequately "fill" the space, or lack of sufficient computational resources. The technique of local variable selection provides a partial solution to these problems by attempting to approximate functions locally using fewer than the complete set of input dimensions.

This paper extends work reported in (Hayashi & Nakai.

I give an introduction to Bayesian networks for AI researchers with a limited grounding in probability theory. Indeed, it is probably fair to say that Bayesian networks are to a large segment of the AI-uncertainty community what resolution theorem proving is to the AIlogic community. Nevertheless, despite what seems to be their obvious importance, the ideas and techniques have not spread much beyond the research community responsible for them. I hope to rectify this situation by making Bayesian networks more accessible to the probabilistically unsophisticated.

Automated diagnosis is an important AI problem not only for its potential practical applications but also because it exposes issues common to all automated reasoning efforts and presents real challenges to existing paradigms. Current research in this area addresses many problems, including managing and structuring probabilistic information, modeling physical systems, reasoning with defeasible assumptions, and interleaving deliberation and action. Furthermore, diagnosis programs must face these problems in contexts where scaling up to deal with cases of realistic size results in daunting combinatorics. This article presents these and other issues as discussed at the First International Workshop on Principles of Diagnosis.

Decision analysis and expert systems are technologies intended to support human reasoning and decision making by formalizing expert knowledge so that it is amenable to mechanized reasoning methods. Despite some common goals, these two paradigms have evolved divergently, with fundamental differences in principle and practice. Recent recognition of the deficiencies of traditional AI techniques for treating uncertainty, coupled with the development of belief nets and influence diagrams, is stimulating renewed enthusiasm among AI researchers in probabilistic reasoning and decision analysis. We present the key ideas of decision analysis and review recent research and applications that aim toward a marriage of these two paradigms. This work combines decision-analytic methods for structuring and encoding uncertain knowledge and preferences with computational techniques from AI for knowledge representation, inference, and explanation. We end by outlining remaining research issues to fully develop the potential of this enterprise.

I give an introduction to Bayesian networks for AI researchers with a limited grounding in probability theory. Over the last few years, this method of reasoning using probabilities has become popular within the AI probability and uncertainty community. Indeed, it is probably fair to say that Bayesian networks are to a large segment of the AI-uncertainty community what resolution theorem proving is to the AIlogic community. Nevertheless, despite what seems to be their obvious importance, the ideas and techniques have not spread much beyond the research community responsible for them. This is probably because the ideas and techniques are not that easy to understand. I hope to rectify this situation by making Bayesian networks more accessible to the probabilistically unsophisticated.

I address practical issues concerning the construction of normative expert systems, and examine the influence diagram as a potential framework for representing knowledge in such systems. I introduce an extension of the influence-diagram representation called a similarity network. A similarity network is a tool for constructing large and complex influence diagrams. The representation allows a user to construct independent influence diagrams for subsets of a given domain. A valid influence diagram for the entire domain can then be constructed from the individual diagrams.

One popular class of unsupervised algorithms are competitive algorithms. In the traditional view of competition, only one competitor, the winner, adapts for any given case. I propose to view competitive adaptation as attempting to fit a blend of simple probability generators (such as gaussians) to a set of data-points. The maximum likelihood fit of a model of this type suggests a "softer" form of competition, in which all competitors adapt in proportion to the relative probability that the input came from each competitor. I investigate one application of the soft competitive model, placement of radial basis function centers for function interpolation, and show that the soft model can give better performance with little additional computational cost. 1 INTRODUCTION Interest in unsupervised learning has increased recently due to the application of more sophisticated mathematical tools (Linsker, 1988; Plumbley and Fallside, 1988; Sanger, 1989) and the success of several elegant simulations of large scale selforganization (Linsker, 1986; Kohonen, 1982). One popular class of unsupervised algorithms are competitive algorithms, which have appeared as components in a variety of systems (Von der Malsburg, 1973; Fukushima, 1975; Grossberg, 1978). Generalizing the definition of Rumelhart and Zipser (1986), a competitive adaptive system consists of a collection of modules which are structurally identical except, possibly, for random initial parameter variation.

In this paper we develop a Bayes criterion which includes the Rissanen complexity, for inferring regular grammar models. We develop two methods for regular grammar Bayesian inference. The fIrst method is based on treating the regular grammar as a I-dimensional Markov source, and the second is based on the combinatoric characteristics of the regular grammar itself. We apply the resulting Bayes criteria to a particular example in order to show the efficiency of each method.