Convergent Message-Passing Algorithms for Inference over General Graphs with Convex Free Energies

TL;DR

This paper introduces two convergent message-passing algorithms for inference in graphical models using convex free energies, overcoming convergence issues of traditional belief propagation in cyclic graphs.

Contribution

It presents two new BP-like algorithms guaranteed to converge to the global minimum for convex free energies on any graph, along with a heuristic for parameter setting.

Findings

Algorithms guarantee convergence to the global minimum.

Applicable to general graphs with cycles.

Improved inference accuracy and stability.

Abstract

Inference problems in graphical models can be represented as a constrained optimization of a free energy function. It is known that when the Bethe free energy is used, the fixedpoints of the belief propagation (BP) algorithm correspond to the local minima of the free energy. However BP fails to converge in many cases of interest. Moreover, the Bethe free energy is non-convex for graphical models with cycles thus introducing great difficulty in deriving efficient algorithms for finding local minima of the free energy for general graphs. In this paper we introduce two efficient BP-like algorithms, one sequential and the other parallel, that are guaranteed to converge to the global minimum, for any graph, over the class of energies known as "convex free energies". In addition, we propose an efficient heuristic for setting the parameters of the convex free energy based on the structure of the graph.