Clamping improves TRW and mean field approximations

In: https://www.repository.cam.ac.uk/handle/1810/255940

Abstract

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. ; NICTA is funded by the Australian Government through the Department of Communications and the Australian Research Council through the ICT Centre of Excellence Program. ; This is the author accepted manuscript. It is currently under an indefinite embargo pending publication by MIT Press.