Gauged Mini-Bucket Elimination for Approximate Inference

TL;DR

This paper introduces WMBE-G, a novel gauge-variational method that combines gauge transformations with weighted mini-bucket elimination to improve bounds on the partition function in graphical models, enhancing inference accuracy.

Contribution

It proposes a new gauge-variational approach, WMBE-G, that provides both bounds on the partition function and is easier to optimize than previous methods.

Findings

WMBE-G strictly improves WMBE for symmetric models.

WMBE-G effectively bounds the partition function in nonsymmetric models.

WMBE-G is easier to optimize than prior gauge-variational algorithms.

Abstract

Computing the partition function $Z$ of a discrete graphical model is a fundamental inference challenge. Since this is computationally intractable, variational approximations are often used in practice. Recently, so-called gauge transformations were used to improve variational lower bounds on $Z$. In this paper, we propose a new gauge-variational approach, termed WMBE-G, which combines gauge transformations with the weighted mini-bucket elimination (WMBE) method. WMBE-G can provide both upper and lower bounds on $Z$, and is easier to optimize than the prior gauge-variational algorithm. We show that WMBE-G strictly improves the earlier WMBE approximation for symmetric models including Ising models with no magnetic field. Our experimental results demonstrate the effectiveness of WMBE-G even for generic, nonsymmetric models.