Gauged mini-bucket elimination for approximate inference

Computing the partition function Z of a discrete graphical model is a fundamental inference challenge. Since this is computationally intractable, variational approximations are often used in practice. Recently, so-called gauge transformations were used to improve variational lower bounds on Z. In this paper, we propose a new gauge-variational approach, termed WMBE-G, which combines gauge transformations with the weighted mini-bucket elimination (WMBE) method. WMBE-G can provide both upper and lower bounds on Z, and is easier to optimize than the prior gauge-variational algorithm. We show that WMBE-G strictly improves the earlier WMBE approximation for symmetric models including Ising models with no magnetic field. Our experimental results demonstrate the effectiveness of WMBE-G even for generic, non-symmetric models.1