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Generalized Belief Propagation on Tree Robust Structured Region Graphs
Andrew Gelfand, Max Welling
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.
Keywords:
Pages: 296-305
PS Link:
PDF Link: /papers/12/p296-gelfand.pdf
BibTex:
@INPROCEEDINGS{Gelfand12,
AUTHOR = "Andrew Gelfand
and Max Welling",
TITLE = "Generalized Belief Propagation on Tree Robust Structured Region Graphs",
BOOKTITLE = "Proceedings of the Twenty-Eighth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-12)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2012",
PAGES = "296--305"
}
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