Generalizing variable elimination in Bayesian networks

This paper describes a generalized version of the variable elimination algorithm for Bayesian networks. Variable elimination computes the marginal probability for some specified set of variables in a network. The algorithm consists of a single pass through a list of data structures called buckets. The generalization presented here adds a second pass to the algorithm and produces the marginal probability density for every variable in the buckets. The algorithm and the presentation focus on algebraic operations, striving for simplicity and easy of understanding. The algorithm has been implemented in the JavaBayes system, a freely distributed system for the construction and manipulation of Bayesian networks.

[1]  Probability functions on complex pedigrees , 1978 .

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

[3]  Prakash P. Shenoy,et al.  Axioms for probability and belief-function proagation , 1990, UAI.

[4]  J. Pearl.  On probability intervals , 1988, Int. J. Approx. Reason..

[5]  Judea Pearl,et al.  Probabilistic reasoning in intelligent systems - networks of plausible inference , 1991, Morgan Kaufmann series in representation and reasoning.

[6]  Uue Kjjrull.  Triangulation of Graphs { Algorithms Giving Small Total State Space Triangulation of Graphs { Algorithms Giving Small Total State Space , 1990 .

[7]  Dan Geiger,et al.  Identifying independence in bayesian networks , 1990, Networks.

[8]  Zhaoyu Li,et al.  Efficient inference in Bayes networks as a combinatorial optimization problem , 1994, Int. J. Approx. Reason..

[9]  Denise Draper,et al.  Clustering Without (Thinking About) Triangulation , 1995, UAI.

[10]  Nevin Lianwen Zhang,et al.  Exploiting Causal Independence in Bayesian Network Inference , 1996, J. Artif. Intell. Res..

[11]  Rina Dechter,et al.  Bucket elimination: A unifying framework for probabilistic inference , 1996, UAI.

[12]  Ross D. Shachter.  Bayes-Ball: The Rational Pastime (for Determining Irrelevance and Requisite Information in Belief Networks and Influence Diagrams) , 1998, UAI.

[13]  Adnan Darwiche,et al.  Dynamic Jointrees , 1998, UAI.