We provide a novel method for Bayesian network inference based upon the idea of pre-compiling a given Bayesian network into a series of SAT instances. We show that this approach allows us to exploit the numerical structure of the problem domain represented by the Bayesian network and that it can be combined with the paradigm of dynamic programming to exploit both the topology and the numerical structure of the network. Because these SAT-based methods exploit both, they are assured of performing better than traditional methods that exploit only the topology of the network (sometimes referred to as "structure-based methods"). A surprising result that follows from our approach is that in domains that exhibit "high" numerical structure, we can remove the "hardness" of the Bayesian inference task into a one-time pre-compilation phase that is independent of any query, thereby achieving a fully polynomial-time randomized approximation scheme (FPRAS) for query-answering. We expect SAT-based approaches to be successful in many practical domains that exhibit good numerical structure (like the presence of monotonic/qualitative relationships between the variables of the domain).
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