Double-cover-based analysis of the Bethe permanent of non-negative matrices

TL;DR

This paper investigates the Bethe approximation of the permanent for non-negative matrices, demonstrating its favorable properties using topological double covers of factor graphs, which could improve approximation methods.

Contribution

It introduces a novel analysis using topological double covers of factor graphs to better understand the Bethe approximation of the permanent.

Findings

Bethe approximation is well-behaved for non-negative matrices

Topological double covers relate to the permanent via factor graph partition functions

Transformation of double covers offers new analytical insights

Abstract

The permanent of a non-negative matrix appears naturally in many information processing scenarios. Because of the intractability of the permanent beyond small matrices, various approximation techniques have been developed in the past. In this paper, we study the Bethe approximation of the permanent and add to the body of literature showing that this approximation is very well behaved in many respects. Our main technical tool are topological double covers of the normal factor graph whose partition function equals the permanent of interest, along with a transformation of these double covers.