图多项式与配分函数的循环置信传播逼近
Graph polynomials and approximation of partition functions with Loopy Belief Propagation
摘要：
Bethe逼近或循环置信传播算法是逼近与图相关的概率模型的分区函数的成功方法。Chertkov和Chernyak导出了一个有趣的公式，称为Loop Series Expansion，这是配分函数的一种扩展。级数的主要项是贝特近似，而其他项则由称为广义环的子图标记。在我们最近的文章中，我们导出了系数为正整数的多项式形式的循环级数展开式，并将结果推广到边缘展开式。本文对所得结果给出了更明确的推导，并讨论了文中所引入的多项式的性质。
英文摘要：
The Bethe approximation, or loopy belief propagation algorithm is a successful method for approximating partition functions of probabilistic models associated with a graph. Chertkov and Chernyak derived an interesting formula called Loop Series Expansion, which is an expansion of the partition function. The main term of the series is the Bethe approximation while other terms are labeled by subgraphs called generalized loops. In our recent paper, we derive the loop series expansion in form of a polynomial with coefficients positive integers, and extend the result to the expansion of marginals. In this paper, we give more clear derivation for the results and discuss the properties of the polynomial which is introduced in the paper.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
