Generalized Belief Propagation on Tree Robust Structured Region Graphs

Andrew E. Gelfand, Max Welling
Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, PMLR R10:294-303, 2012.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR10-gelfand12a, title = {Generalized Belief Propagation on Tree Robust Structured Region Graphs}, author = {Gelfand, Andrew E. and Welling, Max}, booktitle = {Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence}, pages = {294--303}, year = {2012}, editor = {de Freitas, Nando and Murphy, Kevin}, volume = {R10}, series = {Proceedings of Machine Learning Research}, month = {14--18 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r10/main/assets/gelfand12a/gelfand12a.pdf}, url = {https://proceedings.mlr.press/r10/gelfand12a.html}, 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.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Generalized Belief Propagation on Tree Robust Structured Region Graphs %A Andrew E. Gelfand %A Max Welling %B Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2012 %E Nando de Freitas %E Kevin Murphy %F pmlr-vR10-gelfand12a %I PMLR %P 294--303 %U https://proceedings.mlr.press/r10/gelfand12a.html %V R10 %X 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. %Z Reissued by PMLR on 04 October 2026.
APA
Gelfand, A.E. & Welling, M.. (2012). Generalized Belief Propagation on Tree Robust Structured Region Graphs. Proceedings of the 28th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R10:294-303 Available from https://proceedings.mlr.press/r10/gelfand12a.html. Reissued by PMLR on 04 October 2026.

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