Accuracy Bounds for Belief Propagation

TL;DR

This paper derives a simple, computable bound on the error of belief propagation in pairwise Markov random fields, enhancing theoretical understanding of its performance in approximate inference.

Contribution

It introduces a new, practical bound on BP accuracy for binary systems, improving upon previous methods with a simpler and more effective approach.

Findings

Derived a new error bound for BP in binary systems

Bound compares favorably with previous methods

Provides theoretical insights into BP performance

Abstract

The belief propagation (BP) algorithm is widely applied to perform approximate inference on arbitrary graphical models, in part due to its excellent empirical properties and performance. However, little is known theoretically about when this algorithm will perform well. Using recent analysis of convergence and stability properties in BP and new results on approximations in binary systems, we derive a bound on the error in BP's estimates for pairwise Markov random fields over discrete valued random variables. Our bound is relatively simple to compute, and compares favorably with a previous method of bounding the accuracy of BP.