Gauging Variational Inference

TL;DR

This paper introduces Gauged-MF and Gauged-BP, novel variational inference methods that improve partition function estimation in graphical models by using gauge transformations, outperforming traditional mean-field and belief propagation methods.

Contribution

The paper proposes two new variational schemes, G-MF and G-BP, that provide tighter bounds and are exact for certain graph structures, advancing inference techniques in graphical models.

Findings

G-MF and G-BP outperform traditional MF and BP in experiments.

Both methods are exact for single-loop graphs of a specific structure.

Algorithms generalize well to large graphical models with up to 300 variables.

Abstract

Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice, where mean-field (MF) and belief propagation (BP) are arguably the most popular and successful approaches of a variational type. In this paper, we propose two new variational schemes, coined Gauged-MF (G-MF) and Gauged-BP (G-BP), improving MF and BP, respectively. Both provide lower bounds for the partition function by utilizing the so-called gauge transformation which modifies factors of GM while keeping the partition function invariant. Moreover, we prove that both G-MF and G-BP are exact for GMs with a single loop of a special structure, even though the bare MF and BP perform badly in this case. Our extensive experiments, on complete GMs of relatively small size and on large GM (up-to 300 variables) confirm that the newly proposed algorithms outperform and generalize MF and BP.