We examine the effect of clamping variables for approximate inference in undirected graphical models with pairwise relationships and discrete variables. For any number of variable labels, we demonstrate that clamping and summing approximate sub-partition functions can lead only to a decrease in the partition function estimate for TRW, and an increase for the naive mean field method, in each case guaranteeing an improvement in the approximation and bound. We next focus on binary variables, add the Bethe approximation to consideration and examine ways to choose good variables to clamp, introducing new methods. We show the importance of identifying highly frustrated cycles, and of checking the singleton entropy of a variable. We explore the value of our methods by empirical analysis and draw lessons to guide practitioners.

本篇论文研究了在无向图中，基于密集型变量以及对近似推断的影响。对于任意标签数量的变量，文章采用了clamp和sum的逼近子分区函数的方式，证明了在TRW和naive mean field方法中，clamp和sum的逼进子分区函数都会导致分区函数估计下降，引入Bethe逼近来考虑二元变量，并探讨选择良好的clamp变量的方法，研究发现高度受挫的周期和单例信息熵的识别非常重要，最后通过经验分析探讨了我们方法的价值。

夹紧改进TRW和平均场逼近