How long, O Bayesian network, will I sample thee? A program analysis perspective on expected sampling times

TL;DR

This paper presents a method to automatically compute the expected sampling time for Bayesian networks by translating them into probabilistic programs and applying proof rules, aiding in understanding inference efficiency.

Contribution

It introduces a novel approach to analyze expected sampling times in Bayesian networks through program translation and automated proof rules, which was not previously available.

Findings

Successfully analyzed real-world Bayesian networks

Automated computation of expected sampling times

Provides insights into inference efficiency

Abstract

Bayesian networks (BNs) are probabilistic graphical models for describing complex joint probability distributions. The main problem for BNs is inference: Determine the probability of an event given observed evidence. Since exact inference is often infeasible for large BNs, popular approximate inference methods rely on sampling. We study the problem of determining the expected time to obtain a single valid sample from a BN. To this end, we translate the BN together with observations into a probabilistic program. We provide proof rules that yield the exact expected runtime of this program in a fully automated fashion. We implemented our approach and successfully analyzed various real-world BNs taken from the Bayesian network repository.