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We describe a dynamic programming algorithm for computing the marginaldistribution of discrete probabilistic programs. This algorithm takes afunctional interpreter for an arbitrary probabilistic programming language andturns it into an efficient marginalizer. Because direct caching ofsub-distributions is impossible in the presence of recursion, we build a graphof dependencies between sub-distributions. This factored sum-product networkmakes (potentially cyclic) dependencies between subproblems explicit, andcorresponds to a system of equations for the marginal distribution. We solvethese equations by fixed-point iteration in topological order. We illustratethis algorithm on examples used in teaching probabilistic models, computationalcognitive science research, and game theory.

A Dynamic Programming Algorithm for Inference in Recursive Probabilistic Programs