Exact Bayesian Inference for Loopy Probabilistic Programs using Generating Functions
arxiv(2023)
摘要
We present an exact Bayesian inference method for inferring posterior
distributions encoded by probabilistic programs featuring possibly unbounded
loops. Our method is built on a denotational semantics represented by
probability generating functions, which resolves semantic intricacies induced
by intertwining discrete probabilistic loops with conditioning (for encoding
posterior observations). We implement our method in a tool called Prodigy; it
augments existing computer algebra systems with the theory of generating
functions for the (semi-)automatic inference and quantitative verification of
conditioned probabilistic programs. Experimental results show that Prodigy can
handle various infinite-state loopy programs and exhibits comparable
performance to state-of-the-art exact inference tools over loop-free
benchmarks.
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关键词
loopy probabilistic programs,exact bayesian inference
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