Using Tree-Decomposable Structures to Approximate Belief Networks
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.
PDF Link: /papers/93/p376-sarkar.pdf
AUTHOR = "Sumit Sarkar
TITLE = "Using Tree-Decomposable Structures to Approximate Belief Networks",
BOOKTITLE = "Proceedings of the Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-93)",
PUBLISHER = "Morgan Kaufmann",
ADDRESS = "San Francisco, CA",
YEAR = "1993",
PAGES = "376--382"