Generalized Belief Propagation on Tree Robust Structured Region Graphs
| Autor: | Gelfand, Andrew E., Welling, Max |
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| Rok vydání: | 2012 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty in Artificial Intelligence (UAI2012) |
| Databáze: | arXiv |
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