Probabilistic Programming Meets Automata Theory: Exact Inference using Weighted Automata

TL;DR

This paper introduces a novel approach combining probabilistic programming with weighted automata to perform exact inference in certain discrete probabilistic programs, enabling precise analysis of posterior distributions.

Contribution

It develops a method to encode probabilistic programs as weighted automata, allowing exact inference through automata-theoretic operations, a novel integration of these fields.

Findings

Successfully encodes distributions over program variables as weighted automata

Enables exact inference for a class of discrete probabilistic programs

Bridges probabilistic programming and automata theory for quantitative analysis

Abstract

Probabilistic programs encode stochastic models as ordinary-looking programs with primitives for sampling numbers from predefined distributions and conditioning. Their applications include, among many others, machine learning and modeling of autonomous systems. The analysis of probabilistic programs is often quantitative - it involves reasoning about numerical properties like probabilities and expectations. A particularly important quantitative property of probabilistic programs is their posterior distribution, i.e., the distribution over possible outputs for a given input (or prior) distribution. Computing the posterior distribution exactly is known as exact inference. We present our current research using weighted automata, a generalization of the well-known finite automata, for performing exact inference in a restricted class of discrete probabilistic programs. This is achieved by encoding distributions over program variables - possibly with infinite support - as certain weighted automata. The semantics of our programming language then corresponds to common automata-theoretic constructions, such as product, concatenation, and others.