Clamping Improves TRW and Mean Field Approximations
This work provides incremental improvements for practitioners in machine learning and statistics dealing with inference in graphical models.
The paper tackles the problem of improving approximate inference in undirected graphical models by clamping variables, showing that this approach decreases partition function estimates for TRW and increases them for naive mean field, thereby guaranteeing better approximations and bounds.
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.