Value Elimination: Bayesian Inference via Backtracking Search

We present Value Elimination, a new algorithm for Bayesian Inference. Given the same variable order­ ing information, Value Elimination can achieve per­ formance that is within a constant factor of variable elimination or recursive conditioning, and on some problems it can perform exponentially better, irrespec­ tive 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 re­ cursive conditioning; (2) it can utilize all of the logi­ cal reasoning techniques used in state of the art SAT solvers; these techniques allow it to obtain consider­ able extra mileage out of zero entries in the CPTs; (3) it can be naturally and easily extended to take advan­ tage of context specific structure; and (4) it supports dynamic variable orderings which might be particu­ larly advantageous in the presence of context specific structure. We have implemented a version of Value Elimination that demonstrates very promising perfor­ mance, often being one or two orders of magnitude faster than a commercial Bayes inference engine, de­ spite the fact that it does not as yet take advantage of context specific structure.