摘要翻译：
利用循环演算框架，给出了平面图模型近似推论的新结果。循环演算（Chertkov and Chernyak，2006)允许将图形模型的精确配分函数表示为有限项和，一旦信念传播(BP)解已知，就可以计算这些项和。一般说来，对所有校正项的完全求和是困难的。我们为（Certkov et al.，2008)中提出的方法发展了一个算法，它表示了平面图上的一个有效的截断方案，并用矩阵的Pfaffians表示了级数。我们分析了在网格和其他平面图上具有二元变量和成对相互作用的模型的配分函数逼近算法的性能。我们详细研究了循环级数和等价的Pfaffian级数，并证明了对于一般的难解平面模型，Pfaffian级数的第一项可以提供非常精确的近似。该算法的性能优于以往的循环序列截断方案，并且在近似推理方面与其他先进的方法具有竞争力。
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英文标题：
《Approximate inference on planar graphs using Loop Calculus and Belief
  Propagation》
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作者：
V. G\'omez, H. J. Kappen, M. Chertkov
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最新提交年份：
2009
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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：
  We introduce novel results for approximate inference on planar graphical models using the loop calculus framework. The loop calculus (Chertkov and Chernyak, 2006) allows to express the exact partition function of a graphical model as a finite sum of terms that can be evaluated once the belief propagation (BP) solution is known. In general, full summation over all correction terms is intractable. We develop an algorithm for the approach presented in (Certkov et al., 2008) which represents an efficient truncation scheme on planar graphs and a new representation of the series in terms of Pfaffians of matrices. We analyze the performance of the algorithm for the partition function approximation for models with binary variables and pairwise interactions on grids and other planar graphs. We study in detail both the loop series and the equivalent Pfaffian series and show that the first term of the Pfaffian series for the general, intractable planar model, can provide very accurate approximations. The algorithm outperforms previous truncation schemes of the loop series and is competitive with other state-of-the-art methods for approximate inference.
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PDF链接：
https://arxiv.org/pdf/0901.0786