Uncertain Information Processing in Expert Systems systematically and critically examines probabilistic and rule-based (compositional, MYCIN-like) systems, the two most important families of expert systems dealing with uncertainty. The book features a detailed introduction to probabilistic systems (including methods using graphical models and methods of knowledge integration), an analysis of compositional systems based on algebraic considerations, an application of graphical models, and the Dempster-Shafer theory of evidence and its use in expert systems. The book will be useful to anyone working in artificial intelligence, statistical computing, symbolic logic, and expert systems.
PRELIMINARIES: BASIC MATHEMATICAL NOTIONS. PROBABILITY. Basic Notions. Independence and Conditional Probability: Events. Independence and Conditional Probability: Two Random Variates. Independence and Conditional Probabilities: Random Fields. Log-Linear Representations of Probability Distributions of Random Fields. Appendix: Where Does the Probability Come From? GRAPHS AND PROBABILITY. Graphs. From Hierachial Log-Linear Models to Graphical Representation of Probability Distributions of Random Fields. Markov Properties. Decomposability and Collapsibility. Decomposability and Approximation. Appendix: Some Additional Facts Concerning Graphs. DECISION MAKING UNDER UNCERTAINTY. Decision Task. Decision Under Ignorance. Maximum Entropy Principle. Minimax Principle. LOCAL COMPUTATIONS WITH PROBABILITIES ON GRAPHICAL STRUCTURES AND INFLUENCE DIAGRAMS. Causal Graphs and Conditional Probability Tables. Local Representation of Probabilities. Local Computations: Inference Engine. Local Computations: Some Technicalities. Shachter's Method. KNOWLEDGE INTEGRATION METHODS. Completeness of Input Knowledge. Optimal Decision. Lagrange Multiplers Method. Iterative Proportional Fitting Procedure. D.S.S. Approximations. Studeng's Method. AN INTRODUCTION TO COMPOSITIONAL SYSTEMS. Basic Definitions and Assumptions on Compositional Systems. Some Properties of Combining Functions. Backward Chaining. Three-Valued Systems. The Most Modest Runs. Additional Information on Propositional Logic. COMPOSITIONAL SYSTEMS: AN ALGEBRAIC ANALYSIS. Compositional Systems and Ordered Abelian Groups. Comparative Properties of Compositional Systems. Finitely Generated Ordered Abelian Groups. Where Are Weights of Rules From? A PROBABILISTIC ANALYSIS OF COMPOSITIONAL SYSTEMS. Uncertainty and Probability in Classical Systems. Compositional Systems and Log-Linear Representation. Compositional Systems and Graphical Models: The Method of Guarded Use. THE DEMPSTER-SHAFER THEORY OF EVIDENCE AND ITS USE IN EXPERT SYSTEMS. An Introduction to Dempster-Shafer Theory. Dempster-Shafer Theory and Local Computations. Belief Functions and Compositional Systems. ESTIMATION OF PROBABILITIES AND STRUCTURES. Estimation of Probabilities. Estimation of Structures. References.