和积算法收敛的充分条件
Sufficient conditions for convergence of the Sum-Product Algorithm
摘要：
我们推导出新的条件，保证收敛的总和产品算法（也称为循环信念传播或简单的信念传播）到一个唯一的不动点，无论初始消息。条件的计算复杂性是变量数目的多项式。与以前存在的条件相比，我们的结果是直接适用于任意因子图（离散变量），并被证明是有效的，在某些额外的条件下，也在含零因子的情况下。我们比较我们的边界与现有的，数字，如果可能的话，分析。对于具有成对相互作用的二元变量，我们推导出考虑局部证据的充分条件（即，单变量因素）和对相互作用的类型（吸引或排斥）。经验表明，这个界限优于现有的界限。
英文摘要：
We derive novel conditions that guarantee convergence of the Sum-Product algorithm (also known as Loopy Belief Propagation or simply Belief Propagation) to a unique fixed point, irrespective of the initial messages. The computational complexity of the conditions is polynomial in the number of variables. In contrast with previously existing conditions, our results are directly applicable to arbitrary factor graphs (with discrete variables) and are shown to be valid also in the case of factors containing zeros, under some additional conditions. We compare our bounds with existing ones, numerically and, if possible, analytically. For binary variables with pairwise interactions, we derive sufficient conditions that take into account local evidence (i.e., single variable factors) and the type of pair interactions (attractive or repulsive). It is shown empirically that this bound outperforms existing bounds.
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。
