Loop corrections for message passing algorithms in continuous variable models

TL;DR

This paper derives loop correction equations for belief propagation in continuous Gaussian models, offering a new way to compute covariances and relating it to Expectation Propagation for non-Gaussian cases.

Contribution

It introduces a novel loop correction method for belief propagation in continuous models and connects it to Expectation Propagation for perturbed systems.

Findings

Derived equations for Loop Corrected Belief Propagation in Gaussian models

Proposed a new covariance computation method using cavity graphs

Linked loop correction algorithms to Expectation Propagation in nonlinear models

Abstract

In this paper we derive the equations for Loop Corrected Belief Propagation on a continuous variable Gaussian model. Using the exactness of the averages for belief propagation for Gaussian models, a different way of obtaining the covariances is found, based on Belief Propagation on cavity graphs. We discuss the relation of this loop correction algorithm to Expectation Propagation algorithms for the case in which the model is no longer Gaussian, but slightly perturbed by nonlinear terms.