Exact Bayesian Inference for Loopy Probabilistic Programs using Generating Functions

Proceedings of the ACM on Programming Languages, vol. 8, pp. 923–953

Abstract

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.

Authors 4

1. Lutz Klinkenberg Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

2. Mingshuai Chen

   Zhejiang University

   Affiliation as printed

   Zhejiang University, Hangzhou, China

3. Darion Haase Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany

4. Joost-Pieter Katoen Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen University, Aachen, Germany