Value Elimination: Bayesian Interence via Backtracking Search

We present Value Elimination, a new algorithm for Bayesian Inference. Given the same variable ordering information, Value Elimination can achieve performance that is within a constant factor of variable elimination or recursive conditioning, and on some problems it can perform exponentially better, irrespective of the variable ordering used by these algorithms. Value Elimination's other features include: (1) it can achieve the same space-time tradeoff guarantees as recursive conditioning; (2) it can utilize all of the logical reasoning techniques used in state of the art SAT solvers; these techniques allow it to obtain considerable extra mileage out of zero entries in the CPTs; (3) it can be naturally and easily extended to take advantage of context specific structure; and (4) it supports dynamic variable orderings which might be particularly advantageous in the presence of context specific structure. We have implemented a version of Value Elimination that demonstrates very promising performance, often being one or two orders of magnitude faster than a commercial Bayes inference engine, despite the fact that it does not as yet take advantage of context specific structure.