Graph partition strategies for generalized mean field inference

TL;DR

This paper introduces a new approach combining graph partitioning with generalized mean field inference to improve variational approximations in graphical models, supported by formal analysis and empirical results.

Contribution

It presents a novel integration of graph partitioning algorithms with GMF inference, enhancing the optimization of variational approximations in graphical models.

Findings

Weighted MinCut is effective for GMF clustering.

Formal analysis links graph cuts to GMF approximation quality.

Empirical results support the use of specific graph partition strategies.

Abstract

An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph partitioning algorithms with a generalized mean field (GMF) inference algorithm. This combination optimizes over disjoint clustering of variables and performs inference using those clusters. We provide a formal analysis of the relationship between the graph cut and the GMF approximation, and explore several graph partition strategies empirically. Our empirical results provide rather clear support for a weighted version of MinCut as a useful clustering algorithm for GMF inference, which is consistent with the implications from the formal analysis.