Analysis of Bayesian Networks via Prob-Solvable Loops

TL;DR

This paper extends Prob-solvable loops to encode various Bayesian networks, enabling automated solutions for inference, sensitivity analysis, and sampling problems, demonstrated through benchmark evaluations.

Contribution

It introduces new features to Prob-solvable loops for encoding Bayesian networks, allowing automated analysis of BN-related problems.

Findings

Successfully encoded various Bayesian networks as Prob-solvable loops

Automated solutions for inference, sensitivity, and sampling problems achieved

Validated approach on multiple BN benchmarks

Abstract

Prob-solvable loops are probabilistic programs with polynomial assignments over random variables and parametrised distributions, for which the full automation of moment-based invariant generation is decidable. In this paper we extend Prob-solvable loops with new features essential for encoding Bayesian networks (BNs). We show that various BNs, such as discrete, Gaussian, conditional linear Gaussian and dynamic BNs, can be naturally encoded as Prob-solvable loops. Thanks to these encodings, we can automatically solve several BN related problems, including exact inference, sensitivity analysis, filtering and computing the expected number of rejecting samples in sampling-based procedures. We evaluate our work on a number of BN benchmarks, using automated invariant generation within Prob-solvable loop analysis.