Analysis of Double Covers of Factor Graphs

TL;DR

This paper introduces a new technique for analyzing double covers of factor graphs, enhancing understanding of the Bethe approximation used to estimate partition sums in complex graphical models.

Contribution

It presents a novel method for analyzing double covers, providing deeper insights into the Bethe approximation in factor graphs.

Findings

Enhanced understanding of the Bethe approximation

New analytical techniques for double covers

Potential improvements in partition sum estimation

Abstract

Many quantities of interest in communications, signal processing, artificial intelligence, and other areas can be expressed as the partition sum of some factor graph. Although the exact calculation of the partition sum is in many cases intractable, it can often be approximated rather well by the Bethe partition sum. In earlier work, we have shown that graph covers are a useful tool for expressing and analyzing the Bethe approximation. In this paper, we present a novel technique for analyzing double covers, a technique which ultimately leads to a deeper understanding of the Bethe approximation.