Understanding the ratio of the partition sum to its Bethe approximation via double covers
Information Theory
2025-09-25 v1 Combinatorics
math.IT
Statistics Theory
Statistics Theory
Abstract
For various classes of graphical models it has been observed that the ratio of the partition sum to its Bethe approximation is often close to being the square of the ratio of the partition sum to its degree-2 Bethe approximation. This is of relevance because the latter ratio can often better be analyzed and/or quantified than the former ratio. In this paper, we give some justifications for the observed relationship between these two ratios and then analyze these ratios for two classes of log-supermodular graphical models.
Cite
@article{arxiv.2509.19910,
title = {Understanding the ratio of the partition sum to its Bethe approximation via double covers},
author = {Pascal O. Vontobel},
journal= {arXiv preprint arXiv:2509.19910},
year = {2025}
}
Comments
Extended version (including appendices) of a paper appearing in Proc. 2025 IEEE Information Theory Workshop, Sydney, Australia, Sept./Oct., 2025