Efficient inference in Bayes networks as a combinatorial optimization problem

A number of exact algorithms have been developed to perform probabilistic inference in Bayesian belief networks in recent years. The techniques used in these algorithms are closely related to network structures and some of them are not easy to understand and implement. In this paper, we consider the problem from the combinatorial optimization point of view and state that e cient probabilistic inference in a belief network is a problem of nding an optimal factoring given a set of probability distributions. From this viewpoint, previously developed algorithms can be seen as alternate factoring strategies. In this paper, we de ne a combinatorial optimization problem, the optimal factoring problem, and discuss application of this problem in belief networks. We show that optimal factoring provides insight into the key elements of e cient probabilistic inference, and demonstrate simple, easily implemented algorithms with excellent performance.