Scaling Exact Inference for Discrete Probabilistic Programs

TL;DR

This paper introduces Dice, a domain-specific language that enables scalable exact inference for discrete probabilistic programs by leveraging program structure and reduction to weighted model counting, handling hundreds of thousands of variables.

Contribution

The paper presents a novel reduction from discrete probabilistic programs to weighted model counting, allowing exact inference to scale to large programs, which was previously infeasible.

Findings

Dice outperforms prior approaches in inference speed

Exact inference scales to hundreds of thousands of variables

The reduction to WMC is correct and preserves semantics

Abstract

Probabilistic programming languages (PPLs) are an expressive means of representing and reasoning about probabilistic models. The computational challenge of probabilistic inference remains the primary roadblock for applying PPLs in practice. Inference is fundamentally hard, so there is no one-size-fits all solution. In this work, we target scalable inference for an important class of probabilistic programs: those whose probability distributions are discrete. Discrete distributions are common in many fields, including text analysis, network verification, artificial intelligence, and graph analysis, but they prove to be challenging for existing PPLs. We develop a domain-specific probabilistic programming language called Dice that features a new approach to exact discrete probabilistic program inference. Dice exploits program structure in order to factorize inference, enabling us to perform exact inference on probabilistic programs with hundreds of thousands of random variables. Our key technical contribution is a new reduction from discrete probabilistic programs to weighted model counting (WMC). This reduction separates the structure of the distribution from its parameters, enabling logical reasoning tools to exploit that structure for probabilistic inference. We (1) show how to compositionally reduce Dice inference to WMC, (2) prove this compilation correct with respect to a denotational semantics, (3) empirically demonstrate the performance benefits over prior approaches, and (4) analyze the types of structure that allow Dice to scale to large probabilistic programs.