Reference: Cooper, G. F. Bayesian Belief-Network Inference Using Recursive Decomposition. KSL, July, 1992.
Abstract: A Bayesian belief network uses a directed acyclic graph to represent probabilistic dependencies among a set of variables. Typically, performing inference on a belief network involves computing conditional probabilities among variables in the network. We introduce an algorithm for belief-network inference that is based on recursive decomposition. The algorithm recursively bisects a belief network to create a binary tree. The tree then is used for probabilistic inference. We describe the recursive-decomposition inference algorithm in sufficient detail for it to be implemented readily, and we prove the validity of the algorithm. We also link belief-network inference that is based on recursive decomposition to the literature on vertex separators. The recursive divide-and-conquer nature of the recursive-decomposition inference algorithm allows an implementation that is brief and simple; it also facilitates our analysis of the time complexity of the algorithm. A companion paper contains an analysis and evaluation of the inference algorithm on numerous belief network structures.