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The computational burden of probabilistic inference remains a hurdle forapplying probabilistic programming languages to practical problems of interest.In this work, we provide a semantic and algorithmic foundation for efficientexact inference on discrete-valued finite-domain imperative probabilisticprograms. We leverage and generalize efficient inference procedures forBayesian networks, which exploit the structure of the network to decompose theinference task, thereby avoiding full path enumeration. To do this, we firstcompile probabilistic programs to a symbolic representation. Then we adapttechniques from the probabilistic logic programming and artificial intelligencecommunities in order to perform inference on the symbolic representation. Weformalize our approach, prove it sound, and experimentally validate it againstexisting exact and approximate inference techniques. We show that our inferenceapproach is competitive with inference procedures specialized for Bayesiannetworks, thereby expanding the class of probabilistic programs that can bepractically analyzed.

Symbolic Exact Inference for Discrete Probabilistic Programs