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摘要翻译：
本文为广义置信传播(GBP)域图的构造提供了一些新的指导。我们将选择环结构区域图(SRG)的外区域问题与寻找相应的马尔可夫网络的基本圈基问题联系起来。我们还定义了一类新的树-鲁棒环-SRG，它的任一马尔可夫网络的诱导（生成）树上的GBP是精确的，由离树交互作用为零得到。然后将这类SRG映射到一个等价的基于马尔可夫网络的树-鲁棒循环基类。通过证明对于每一个圈子集，只参与一个圈的边所得到的图是多重连通的，我们证明了treerobust圈基可以被识别出来。利用这一点，我们确定了两类树型鲁棒循环基：平面循环基和“星形”循环基。在实验中，我们发现树的鲁棒性可以作为一个设计原则来提高GBP的精度和收敛性。
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英文标题：
《Generalized Belief Propagation on Tree Robust Structured Region Graphs》
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作者：
Andrew E. Gelfand, Max Welling
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最新提交年份：
2012
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分类信息：
一级分类：Computer Science 计算机科学
二级分类：Artificial Intelligence 人工智能
分类描述：Covers all areas of AI except Vision, Robotics, Machine Learning, Multiagent Systems, and Computation and Language (Natural Language Processing), which have separate subject areas. In particular, includes Expert Systems, Theorem Proving (although this may overlap with Logic in Computer Science), Knowledge Representation, Planning, and Uncertainty in AI. Roughly includes material in ACM Subject Classes I.2.0, I.2.1, I.2.3, I.2.4, I.2.8, and I.2.11.
涵盖了人工智能的所有领域，除了视觉、机器人、机器学习、多智能体系统以及计算和语言（自然语言处理），这些领域有独立的学科领域。特别地，包括专家系统，定理证明（尽管这可能与计算机科学中的逻辑重叠），知识表示，规划，和人工智能中的不确定性。大致包括ACM学科类I.2.0、I.2.1、I.2.3、I.2.4、I.2.8和I.2.11中的材料。
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英文摘要：
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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PDF链接：
https://arxiv.org/pdf/1210.4857
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