Convexifying the Bethe Free Energy

TL;DR

This paper explores convexified free energy approximations for loopy belief propagation, aiming to improve convergence and quality, but finds that traditional LBP still often outperforms these convex variants in practice.

Contribution

The paper proposes new convexified free energy approximations that directly approximate the Bethe free energy, comparing favorably with existing convex methods.

Findings

Convexified free energies can approximate the Bethe free energy effectively.

Empirical results show LBP often outperforms convex variants in various settings.

The proposed methods compare favorably with state-of-the-art convex free energy approximations.

Abstract

The introduction of loopy belief propagation (LBP) revitalized the application of graphical models in many domains. Many recent works present improvements on the basic LBP algorithm in an attempt to overcome convergence and local optima problems. Notable among these are convexified free energy approximations that lead to inference procedures with provable convergence and quality properties. However, empirically LBP still outperforms most of its convex variants in a variety of settings, as we also demonstrate here. Motivated by this fact we seek convexified free energies that directly approximate the Bethe free energy. We show that the proposed approximations compare favorably with state-of-the art convex free energy approximations.