Spring 1996 Rutgers University 26:010:685

Glenn Shafer
Office: 302B Ackerson Hall, Newark Campus
Telephone: 201-648-1604
E-mail: gshafer@andromeda.rutgers.edu
WWW: http://www.rutgers.edu/Accounting/raw/gsm/shafer.htm

Probabilistic expert systems are increasingly popular for a wide variety of monitoring and diagnostic tasks. Students considering this course who want more perspective on the topic may wish to visit two World Wide Web sites:

http://www.auai.org/

This is the site for the annual Conference on Uncertainty in Artificial Intelligence, which plays a leading role in the development of probabilistic expert systems.

http://www.vuse.vanderbilt.edu/verb+~+dfisher/ai-stats/society.html

This is the site for the biennial International Workshop on Artificial Intelligence and Statistics, which is also devoted in part to managing uncertainty in expert systems.

Other sources, available in the library (or for consultation in the instructor's office), include the now classic book by Judea Pearl, "Probabilistic Reasoning in Intelligent Systems" (1988), and the book of readings edited by Pearl and Shafer, "Readings in Uncertain Reasoning," (1990), both published by Morgan Kaufmann.

The course has a theoretical and a practical side. On the theoretical side, it emphasizes causal modeling. On the practical side, it emphasizes applications to auditing. It is a doctoral course, but it is open to interested masters students. The only prerequisite is a calculus-based course in probability theory.

Materials for the class will be drawn in part from recent research articles, including articles in the proceedings of the two conferences just cited. The class will also draw material from several forthcoming books, including Steffen Lauritzen's Graphical Models, and two new books by the instructor, The Art of Causal Conjecture (MIT Press) and Probabilistic Expert Systems (SIAM).

Meeting time and place to be arranged

Please contact the instructor by or e-mail or telephone if you are interested in the course. The meeting time for the class will be chosen to accomodate as many interested students as possible. There will probably be an organizational meeting in the instructor's office at 2:00 p.m. on Monday, January 15.

Week 1 Introduction to Causality in Probability Trees

Probability trees provide a flexible and easily understood framework for concepts of causality used in probabilistic expert systems and statistics. Especially important is the distinction between variable causes-contingencies permitted by a causal system, and invariant causes-invariants of the system itself. Material for this class will be drawn from the instructor's Art of Causal Conjecture.

Week 2 Introduction to Graphical Models

Most probabilistic expert systems use statistical models based on graphs. Similar graphs have been used in the social sciences, where they are called path diagrams, but in the case of expert systems, most models are discrete. Some graphical models use directed graphs, some use undirected graphs, and some use chain graphs, graphs that are partly directed and partly undirected. Reference: Steffen Lauritzen's Graphical Models.

Week 3 The Causal Interpretation of Graphical Models

The graphical models studied in Week 2 can be understood in terms of the probability trees studied in Week 1. This is the essence of the causal interpretation of these models, and hence provides a basis for the judgments needed to construct them. Reference: Chapter 15 of The Art of Causal Conjecture.

Week 4 Constructing Probabilistic Expert Systems.

This week will concentrate on practical issues in constructing probabilistic expert systems. This includes methods for hypothesizing unobserved variables and for eliciting probabilities from experts.

Week 5 Computation in Probabilistic Expert Systems

Probabilistic expert systems are practical because the directed graphs on which they are based can be transformed into undirected "triangulated" graphs or "join trees," which provide the basis for efficient computation of marginal and posterior probabilities. The material for this class is drawn from the author's Probabilistic Expert Systems.

Week 6 Learning Graphical Models from Data

When sufficient data is available, we prefer to base graphical models more on this data and less on expert judgment. In order to understand how this is done, we need to delve further into graphical representation of probability and the theory of conditional independence. This topic was pioneered by Pearl. Lauritzen's book is also a good reference.

Week 7 Decision Trees and Influence Diagrams

The generalization of probability trees to decision trees has been a standard topic in management science since the publication of Howard Raiffa's Decision Analysis in 1968. The corresponding generalization of the directed acyclic graphs used in probabilistic expert systems is the "influence diagram." The computational tricks used in probabilistic expert systems have been extended to influence diagrams in various ways.

Week 8 Applications to Auditing and Data Mining

The causal models underlying audit reasoning can be represented by probability trees and sometimes by directed acyclic graphs. We will study the representation of analytic review, tests of internal controls, and judgmental sampling. Time permitting, we will also explore a more difficult topic: the probability-tree representation of invoice data and its use for data mining.

Week 9 Hidden Markov Models and Other Generalizations

A major limitation of standard probabilistic systems is their standard multivariate nature; all variables must always be defined. Alternative methods have been developed, especially for speech recognition, that avoid this limitation. We will study some of these methods, especially those based on hidden Markov models.

Week 10 Principles of Causal Conjecture

The principles of causality that inform probabilistic expert systems are also useful in understanding contentious issues that arise in causal inference in epidemiology and the social sciences. This class will be devoted to those issues. Reference: Chapter 14 of The Art of Causal Conjecture.

Week 11 Undirected Graphical Models

Some probabilistic methods in artificial intelligence, especially in image analysis, use undirected rather than directed graphs. We will review this topic using material from Lauritzen's book and from classic articles.

Week 12 Introduction to Belief Functions.

When causal modeling is not feasible, experts are often uncomfortable with the extensive probability judgments required by purely probabilistic systems. The "Dempster-Shafer" theory of belief functions, pioneered by the author 20 years ago, is often used in this case. This class will cover the basics of the theory.

Week 13 Computation with Belief Functions

The computational methods used by probabilistic expert systems extend to belief functions and to certain other methods as well. This class will review the extension and explore its limits. Reference: Probabilistic Expert Systems.