Convexifying the Bethe Free Energy
This work addresses convergence and quality problems in graphical model inference for domains like computer vision and machine learning, but it is incremental as it builds on existing convex free energy methods.
The authors tackled the problem of loopy belief propagation's convergence and local optima issues by developing convexified free energy approximations that directly approximate the Bethe free energy, showing they compare favorably with state-of-the-art convex approximations.
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.