Belief Propagation by Message Passing in Junction Trees: Computing Each Message Faster Using GPU Parallelization

TL;DR

This paper introduces a GPU-accelerated method for belief propagation in junction trees, significantly speeding up computations in Bayesian networks by parallelizing message calculations.

Contribution

It presents a novel GPU-based parallel algorithm for belief propagation in junction trees, improving computational efficiency over traditional methods.

Findings

Achieved speedups from 0.68x to 9.18x on various Bayesian networks.

Developed new data structures and algorithms for parallel message computation.

Analyzed how junction tree parameters influence parallelization and performance.

Abstract

Compiling Bayesian networks (BNs) to junction trees and performing belief propagation over them is among the most prominent approaches to computing posteriors in BNs. However, belief propagation over junction tree is known to be computationally intensive in the general case. Its complexity may increase dramatically with the connectivity and state space cardinality of Bayesian network nodes. In this paper, we address this computational challenge using GPU parallelization. We develop data structures and algorithms that extend existing junction tree techniques, and specifically develop a novel approach to computing each belief propagation message in parallel. We implement our approach on an NVIDIA GPU and test it using BNs from several applications. Experimentally, we study how junction tree parameters affect parallelization opportunities and hence the performance of our algorithm. We achieve speedups ranging from 0.68 to 9.18 for the BNs studied.