Exact Bayesian Inference for Loopy Probabilistic Programs using Generating Functions

TL;DR

This paper introduces Prodigy, a tool for exact Bayesian inference in probabilistic programs with potentially infinite loops, using probability generating functions to handle complex semantics and enable precise posterior computation.

Contribution

It develops a novel semantics based on generating functions for probabilistic programs with loops, allowing exact inference and verification.

Findings

Handles infinite-state loopy programs effectively.

Performs comparably to existing tools on loop-free benchmarks.

Enables semi-automatic inference for complex probabilistic models.

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.