  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.
