对数超模图模型的Bethe配分函数
The Bethe Partition Function of Log-supermodular Graphical Models
摘要：
Sudderth、Wainwright和Willsky已经证明，Bethe近似对应于一个有吸引力的成对二进制图模型上的置信传播算法的任何不动点，提供了真实配分函数的下界。在这项工作中，我们解决了这个猜想的肯定证明，任何图形模型与二进制变量的潜在功能（不一定成对）都是对数超模，贝特分区函数总是下界的真正的分区函数。这一结果的证明来自于“四个函数”定理的一个新的变体，它可能是独立的。
英文摘要：
Sudderth, Wainwright, and Willsky have conjectured that the Bethe approximation corresponding to any fixed point of the belief propagation algorithm over an attractive, pairwise binary graphical model provides a lower bound on the true partition function. In this work, we resolve this conjecture in the affirmative by demonstrating that, for any graphical model with binary variables whose potential functions (not necessarily pairwise) are all log-supermodular, the Bethe partition function always lower bounds the true partition function. The proof of this result follows from a new variant of the "four functions" theorem that may be of independent interest.
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。
