Approximate Inference and Constrained Optimization

TL;DR

This paper introduces a class of algorithms for approximate inference in probabilistic graphical models that optimize Kikuchi free energy through convex bounds, achieving faster convergence than existing methods.

Contribution

It proposes a novel approach using convex bounds for Kikuchi free energy minimization, improving convergence speed over traditional algorithms like CCCP.

Findings

Tighter convex bounds lead to faster algorithms.

The proposed methods outperform CCCP in speed.

Simulations demonstrate significant speed-ups.

Abstract

Loopy and generalized belief propagation are popular algorithms for approximate inference in Markov random fields and Bayesian networks. Fixed points of these algorithms correspond to extrema of the Bethe and Kikuchi free energy. However, belief propagation does not always converge, which explains the need for approaches that explicitly minimize the Kikuchi/Bethe free energy, such as CCCP and UPS. Here we describe a class of algorithms that solves this typically nonconvex constrained minimization of the Kikuchi free energy through a sequence of convex constrained minimizations of upper bounds on the Kikuchi free energy. Intuitively one would expect tighter bounds to lead to faster algorithms, which is indeed convincingly demonstrated in our simulations. Several ideas are applied to obtain tight convex bounds that yield dramatic speed-ups over CCCP.