Refuting Equivalence in Probabilistic Programs with Conditioning

TL;DR

This paper introduces a fully automated, provably correct method for refuting equivalence of probabilistic programs with conditioning, using a novel weighted restarting transformation, demonstrated on probabilistic inference examples.

Contribution

The paper presents the first automated and correct method for refuting equivalence in probabilistic programs with conditioning, based on a new weighted restarting transformation.

Findings

Method successfully refutes equivalence in tested programs.

Weighted restarting transforms conditioned programs into unconditioned ones.

Demonstrated applicability on probabilistic inference benchmarks.

Abstract

We consider the problem of refuting equivalence of probabilistic programs, i.e., the problem of proving that two probabilistic programs induce different output distributions. We study this problem in the context of programs with conditioning (i.e., with observe and score statements), where the output distribution is conditioned by the event that all the observe statements along a run evaluate to true, and where the probability densities of different runs may be updated via the score statements. Building on a recent work on programs without conditioning, we present a new equivalence refutation method for programs with conditioning. Our method is based on weighted restarting, a novel transformation of probabilistic programs with conditioning to the output equivalent probabilistic programs without conditioning that we introduce in this work. Our method is the first to be both a) fully automated, and b) providing provably correct answers. We demonstrate the applicability of our method on a set of programs from the probabilistic inference literature.