1999 ProbabilisticNetworksAndExpertSystems

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Subject Headings: Probabilistic Network, Probabilistic Network Model, Expert System.

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Book Overview

Probabilistic expert systems are graphical networks that support the modelling of uncertainty and decisions in large complex domains, while retaining ease of calculation. Building on original research by the authors over a number of years, this book gives a thorough and rigorous mathematical treatment of the underlying ideas, structures, and algorithms, emphasizing those cases in which exact answers are obtainable. It covers both the updating of probabilistic uncertainty in the light of new evidence, and statistical inference, about unknown probabilities or unknown model structure, in the light of new data. The careful attention to detail will make this work an important reference source for all those involved in the theory and applications of probabilistic expert systems.

This book was awarded the first DeGroot Prize by the International Society for Bayesian Analysis for a book making an important, timely, thorough, and notably original contribution to the statistics literature.

 Robert G. Cowell is a Lecturer in the Faculty of Actuarial Science and Insurance of the Sir John Cass Business School, City of London. He has been working on probabilistic expert systems since 1989.

 A. Philip Dawid is Professor of Statistics at Cambridge University. He has served as Editor of the Journal of the Royal Statistical Society (Series B), Biometrika and Bayesian Analysis, and as President of the International Society for Bayesian Analysis. He holds the Royal Statistical Society Guy Medal in Bronze and in Silver, and the Snedecor Award for the Best Publication in Biometry.

 Steffen L. Lauritzen is Professor of Statistics at the University of Oxford. He has served as Editor of the Scandinavian Journal of Statistics. He holds the Royal Statistical Society Guy Medal in Silver and is an Honorary Fellow of the same society. He has, jointly with David J. Spiegelhalter, received the American Statistical Association’s award for an “Outstanding Statistical Application.”

 David J. Spiegelhalter is Winton Professor of the Public Understanding of Risk at Cambridge University and Senior Scientist in the MRC Biostatistics Unit, Cambridge. He has published extensively on Bayesian methodology and applications, and holds the Royal Statistical Society Guy Medal in Bronze and in Silver.

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Preface

This book arises out of a long-standing collaboration between the authors, which began in 1985 when a subset of us discussed the potential connection between graphical modelling in contingency tables and the type of diagrams being used to represent qualitative knowledge in expert systems. Our various enthusiasms for multivariate analysis, Bayesian statistics, computer algorithms, conditional independence, graph theory, decision-support systems, and so on, have since found a common area of application in probabilistic networks for expert systems, and we have been fortunate to enjoy a long and fruitful period of joint work which has been little hindered by the intervening North Sea. Over this time we have benefited greatly from interactions with a range of researchers who are too numerous to list individually, although for both their scholarly insights and personal good company we must mention David Heckerman, Judea Pearl, Glenn Shafer, Prakash Shenoy, Jim Smith, Joe Whittaker, and the Danes in the ODIN group, particularly Stig Andersen, Finn Jensen, Frank Jensen, Uffe Kjærulff, and Kristian Olesen. Financial support has been received at various times from the European Community SCIENCE fund, the UK Engineering and Physical Science Research Council, Glaxo Pharmaceuticals, the Danish Research Councils through the PIFT programme, and all our home institutions. Finally, we would like to thank our families for putting up (usually in good humour) with the numerous meetings, visits, and late nights that this collaboration has entailed.

1. Introduction

1.1. What is this book about?

The term expert system is perhaps an anachronism in 1999, but is a convenient label for a computer program intended to provide reasoned guidance on some complex but fairly tightly delineated task. The appropriate way of dealing with the many sources of uncertainty in such problems has long been a matter of dispute, but since the late 1980s, particularly following the publication of Judea Pearl’s classic text (Pearl 1988), a fully probabilistic approach has steadily gained acceptance.

The crucial realization of Pearl and others was that ‘'brute force'’ probabilistic manipulations in high-dimensional problems could never become either technically feasible or substantively acceptable, and that the path ahead was to find some way of introducing ‘modularity’, so enabling a large and complex model, and its associated calculations, to be split up into small manageable pieces. The best way to do this turns out to be through the imposition of meaningful simplifying conditional independence assumptions. These, in turn, can be expressed by means of a powerful and appealing graphical representation, and the resulting networks are often termed Bayesian networks, although in this book we prefer the term probabilistic networks, reflecting an increased generality in the representations we consider. Such graphs not only provide an attractive means for modelling and communicating complex structures, but also form the basis for efficient algorithms, both for propagating evidence and for learning about parameters.

Over the last ten years there has been a steady shift in the focus of attention from algorithms for propagating evidence towards methods for learning parameters and structure from data. This has been accompanied by a broadening of scope, into the general area of graphical modelling: a term with its roots in Statistics, but which also incorporates neural networks, hidden Markov models, and many other techniques that exploit conditional independence properties for modelling, display, and computation. The range of researchers now involved in this field, from Computer Science, Engineering, Statistics and the Social Sciences, amongst others, has ensured an exciting and diverse research environment. Nevertheless, we believe that there is still a particular contribution to be made from the statistical perspective emphasizing the generality of the concepts and attempting to place them on a rigorous footing.

2. Logic, Uncertainty, and Probability

2.1 What is an expert system?

  • The Concise Oxford English Dictionary defines expert as "person having special skill or knowledge.” Informally, an expert is someone you turn to when you are faced with a problem that is too difficult for you to solve on your own or that is outside your own particular are of specialized knowledge, and whom you trust to reach a better solution to your problem that you could yourself. Expert systems are attempts to crystallize and codify the knowledge and skills of one or more experts into a tool that can be used by non-specialists. Usually this will be some for of computer problem, but this need not be the case.
  • An expert system consists of two parts, summed up in the equation:
    • Expert System = Knowledge Base + Inference Engine.
  • The knowledge base contains the domain-specific knowledge of a problem, encoded in some manner. The inference engine consists of one or more algorithms for processing the encoded knowledge of the knowledge based together with any further specific information at hand for a given application.

3. Building and Using Probabilistic Networks

4. Graph Theory

5. Markov Properties on Graphs

6. Discrete Networks

7. Gaussian and Mixed Discrete-Gaussian Networks

8. Discrete Multistage Decision Networks

9. Learning About Probabilities

10. Checking Models Against Data

11. Structural Learning

Epilogue

It should be clear, particularly from the last chapter of this book, that the field of probabilistic networks and expert systems is developing rapidly, and no overview could hope to stay up-to-date for long. For this reason we have deliberately chosen to focus on a solid exposition of a limited class of issues, with some confidence that the fundamental methodology will remain of interest and continue to provide a basis for insights into the new challenges that will come about.

Such challenges are arising as the ideas associated with probabilistic expert systems spread far beyond their original focus on fixed networks of discrete variables with precisely specified probabilities. Real applications increasingly feature uncertainty about both quantitative and structural aspects of the model, possibly incomplete data, and a mixture of discrete and continuous nodes whose parent-child relationships may need to be expressed as statistical models. Dynamic networks, in which the structure changes in order to model some underlying evolving process, are a particularly important development whose application extends into the broader arena of signal processing and on-line monitoring.

The problems associated with such models are being tackled by a variety of professional disciplines, which makes the research area very exciting but also difficult to predict. Current developments suggest that the future will see an increasingly unified approach to complex stochastic systems that exploit conditional independence both for graphical representation and as a foundation for computation, and this perspective will incorporate artificial intelligence, signal processing, Bayesian statistics, machine learning, and a host of other disparate topics. By laying out a firm foundation for some of the core ideas in probabilistic networks, we hope that we will have helped others to extend their application to currently unimagined horizons.

Appendix A: Conjugate Analysis for Discrete Data

Appendix B: Gibbs Sampling

Appendix C: Information and Software on the World Wide Web

References

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 AuthorvolumeDate ValuetitletypejournaltitleUrldoinoteyear
1999 ProbabilisticNetworksAndExpertSystemsRobert Cowell
A. Philip Dawid
Steffen Lauritzen
David Spiegelhalter		Probabilistic Networks and Expert SystemsSpringerhttp://books.google.com/books?id=X4KiAKDygOIC1999
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