Exploiting Structure in Weighted Model Counting Approaches to
  Probabilistic Inference
  Previous studies have demonstrated that encoding a Bayesian network into a
SAT formula and then performing weighted model counting using a backtracking
search algorithm can be an effective method for exact inference. In this paper,
we present techniques for improving this approach for Bayesian networks with
noisy-OR and noisy-MAX relations---two relations that are widely used in
practice as they can dramatically reduce the number of probabilities one needs
to specify. In particular, we present two SAT encodings for noisy-OR and two
encodings for noisy-MAX that exploit the structure or semantics of the
relations to improve both time and space efficiency, and we prove the
correctness of the encodings. We experimentally evaluated our techniques on
large-scale real and randomly generated Bayesian networks. On these benchmarks,
our techniques gave speedups of up to two orders of magnitude over the best
previous approaches for networks with noisy-OR/MAX relations and scaled up to
larger networks. As well, our techniques extend the weighted model counting
approach for exact inference to networks that were previously intractable for
the approach.
