Approximate Inference and Constrained Optimization
This addresses convergence issues in approximate inference for Markov random fields and Bayesian networks, offering a more efficient solution for researchers and practitioners in machine learning, though it appears incremental as it builds on prior optimization methods.
The paper tackles the problem of nonconvergence in belief propagation algorithms for approximate inference by introducing a method that minimizes the Kikuchi free energy through convex constrained minimizations of upper bounds, resulting in dramatic speed-ups over existing approaches like CCCP in simulations.
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.