Distributed Convergence Verification for Gaussian Belief Propagation

TL;DR

This paper introduces a new distributed method to verify the convergence of Gaussian belief propagation, enabling scalable inference in large networks without centralized information gathering.

Contribution

It proposes a novel distributed convergence condition for Gaussian BP applicable to various models, verified analytically to suit network topologies.

Findings

The convergence condition is easily verifiable in a distributed manner.

Applicable to pairwise linear Gaussian models and Gaussian Markov random fields.

Enhances the scalability and reliability of Gaussian BP in large-scale networks.

Abstract

Gaussian belief propagation (BP) is a computationally efficient method to approximate the marginal distribution and has been widely used for inference with high dimensional data as well as distributed estimation in large-scale networks. However, the convergence of Gaussian BP is still an open issue. Though sufficient convergence conditions have been studied in the literature, verifying these conditions requires gathering all the information over the whole network, which defeats the main advantage of distributed computing by using Gaussian BP. In this paper, we propose a novel sufficient convergence condition for Gaussian BP that applies to both the pairwise linear Gaussian model and to Gaussian Markov random fields. We show analytically that this sufficient convergence condition can be easily verified in a distributed way that satisfies the network topology constraint.