Using tree-decomposable structures to approximate belief networks

Authors:
Sumit Sarkar
Affiliations:
Department of Quantitative Business Analysis, College of Business Administration, Louisiana State University, Baton Rouge, LA
Venue:
UAI'93 Proceedings of the Ninth international conference on Uncertainty in artificial intelligence
Year:
1993

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Abstract

Tree structures have been shown to provide an efficient framework for propagating beliefs [Pearl, 1986]. This paper studies the problem of finding an optimal approximating tree. The star-decomposition scheme for sets of three binary variables [Lazarsfeld, 1966; Pearl, 1986] is shown to enhance the class of probability distributions that can support tree structures; such structures are called tree-decomposable structures. The logarithm scoring rule is found to be an appropriate optimality criterion to evaluate different tree-decomposable structures. Characteristics of such structures closest to the actual belief network are identified using the logarithm rule, and greedy and exact techniques are developed to find the optimal approximation.