Gauged Mini-Bucket Elimination for Approximate Inference
This work addresses the challenge of approximate inference in graphical models for researchers and practitioners in machine learning, representing an incremental improvement over prior variational methods.
The paper tackled the problem of approximating the partition function in discrete graphical models, which is computationally intractable, by proposing WMBE-G, a method combining gauge transformations with weighted mini-bucket elimination to provide both upper and lower bounds. The result showed that WMBE-G strictly improves earlier approximations for symmetric models like Ising models and is effective for generic models.
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, nonsymmetric models.