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arXiv · 1210.4857

Generalized Belief Propagation on Tree Robust Structured Region Graphs

Andrew E. Gelfand·Max Welling
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Abstract

This paper provides some new guidance in the construction of region graphs for Generalized Belief Propagation (GBP). We connect the problem of choosing the outer regions of a LoopStructured Region Graph (SRG) to that of finding a fundamental cycle basis of the corresponding Markov network. We also define a new class of tree-robust Loop-SRG for which GBP on any induced (spanning) tree of the Markov network, obtained by setting to zero the off-tree interactions, is exact. This class of SRG is then mapped to an equivalent class of tree-robust cycle bases on the Markov network. We show that a treerobust cycle basis can be identified by proving that for every subset of cycles, the graph obtained from the edges that participate in a single cycle only, is multiply connected. Using this we identify two classes of tree-robust cycle bases: planar cycle bases and "star" cycle bases. In experiments we show that tree-robustness can be successfully exploited as a design principle to improve the accuracy and convergence of GBP.

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Andrew E. Gelfand, Max Welling. 2012-10-16. Generalized Belief Propagation on Tree Robust Structured Region Graphs. https://arxiv.org/abs/1210.4857

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