Graph partition strategies for generalized mean field inference
This work addresses the challenge of scalable inference in probabilistic graphical models, though it appears incremental as it builds on existing methods.
The paper tackles the problem of optimizing variational approximations for arbitrary graphical models by combining graph partitioning algorithms with generalized mean field inference, and finds that a weighted MinCut strategy is empirically effective.
An autonomous variational inference algorithm for arbitrary graphical models requires the ability to optimize variational approximations over the space of model parameters as well as over the choice of tractable families used for the variational approximation. In this paper, we present a novel combination of graph partitioning algorithms with a generalized mean field (GMF) inference algorithm. This combination optimizes over disjoint clustering of variables and performs inference using those clusters. We provide a formal analysis of the relationship between the graph cut and the GMF approximation, and explore several graph partition strategies empirically. Our empirical results provide rather clear support for a weighted version of MinCut as a useful clustering algorithm for GMF inference, which is consistent with the implications from the formal analysis.