Constructing probabilistic models.

Bayesian networks have become one of the most popular probabilistic techniques in AI, largely due to the development of several efficient inference algorithms. In this paper we describe a heuristic method for constructing Bayesian networks. Our construction method relies on the relationship between Bayesian networks and decomposable models, a special kind of graphical model. We explain this relationship and then show how it can be used to facilitate model construction. Finally, we describe an implemented computer program that illustrates these ideas.

[1]  Robert E. Tarjan,et al.  Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1984, SIAM J. Comput..

[2]  Peter C. Cheeseman,et al.  In Defense of Probability , 1985, IJCAI.

[3]  W. Deming,et al.  On a Least Squares Adjustment of a Sampled Frequency Table When the Expected Marginal Totals are Known , 1940 .

[4]  Radim Jirousek,et al.  Solution of the marginal problem and decomposable distributions , 1991, Kybernetika.

[5]  Andrew P. Sage,et al.  Uncertainty in Artificial Intelligence , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[6]  D. Rubin,et al.  Statistical Analysis with Missing Data. , 1989 .

[7]  David J. Spiegelhalter,et al.  Local computations with probabilities on graphical structures and their application to expert systems , 1990 .

[8]  R. Jirousek,et al.  On the effective implementation of the iterative proportional fitting procedure , 1995 .

[9]  Ross D. Shachter.  Intelligent Probabilistic Inference , 1985, UAI.

[10]  Ross D. Shachter.  Evaluating Influence Diagrams , 1986, Oper. Res..

[11]  Petr Hájek,et al.  Uncertain information processing in expert systems , 1992 .

[12]  Remco R. Bouckaert,et al.  Probalistic Network Construction Using the Minimum Description Length Principle , 1993, ECSQARU.

[13]  Robert E. Tarjan,et al.  Addendum: Simple Linear-Time Algorithms to Test Chordality of Graphs, Test Acyclicity of Hypergraphs, and Selectively Reduce Acyclic Hypergraphs , 1985, SIAM J. Comput..

[14]  Peter C. Cheeseman,et al.  A Method of Computing Generalized Bayesian Probability Values for Expert Systems , 1983, IJCAI.

[15]  Ross D. Shachter.  Probabilistic Inference and Influence Diagrams , 1988, Oper. Res..

[16]  I. Csiszár.  $I$-Divergence Geometry of Probability Distributions and Minimization Problems , 1975 .

[17]  David Maxwell Chickering,et al.  Learning Bayesian networks: The combination of knowledge and statistical data , 1995, Mach. Learn..

[18]  Finn Verner Jensen,et al.  Introduction to Bayesian Networks , 2008, Innovations in Bayesian Networks.

[19]  David Heckerman,et al.  Decision-theoretic troubleshooting , 1995, CACM.

[20]  Wai Lam,et al.  LEARNING BAYESIAN BELIEF NETWORKS: AN APPROACH BASED ON THE MDL PRINCIPLE , 1994, Comput. Intell..