Convergent Propagation Algorithms via Oriented Trees

TL;DR

This paper introduces an oriented tree decomposition algorithm for graphical model inference that guarantees convergence to the global optimum of the Tree-Reweighted variational problem by performing local updates in the convex dual.

Contribution

The paper presents a novel oriented tree decomposition algorithm with convergence guarantees for solving the TRW variational problem in graphical models.

Findings

Guarantees convergence to the global optimum of the TRW problem.

Performs local updates in the convex dual of the TRW problem.

Uses oriented reparametrization operations that preserve the distribution.

Abstract

Inference problems in graphical models are often approximated by casting them as constrained optimization problems. Message passing algorithms, such as belief propagation, have previously been suggested as methods for solving these optimization problems. However, there are few convergence guarantees for such algorithms, and the algorithms are therefore not guaranteed to solve the corresponding optimization problem. Here we present an oriented tree decomposition algorithm that is guaranteed to converge to the global optimum of the Tree-Reweighted (TRW) variational problem. Our algorithm performs local updates in the convex dual of the TRW problem - an unconstrained generalized geometric program. Primal updates, also local, correspond to oriented reparametrization operations that leave the distribution intact.