Bucket Elimination: A Unifying Framework for Several Probabilistic Inference

Probabilistic inference algorithms for finding the most probable explanation, the maximum aposteriori hypothesis, and the maximum expected utility and for updating belief are reformulated as an elimination--type algorithm called bucket elimination. This emphasizes the principle common to many of the algorithms appearing in that literature and clarifies their relationship to nonserial dynamic programming algorithms. We also present a general way of combining conditioning and elimination within this framework. Bounds on complexity are given for all the algorithms as a function of the problem's structure.