Clamping Improves TRW and Mean Field Approximations

TL;DR

This paper investigates how clamping variables can improve approximate inference methods like TRW and mean field in graphical models, providing theoretical guarantees and practical methods for better bounds.

Contribution

It introduces new methods for selecting variables to clamp, especially in binary models, and demonstrates how to improve approximation bounds in graphical models.

Findings

Clamping improves TRW and mean field bounds in practice.

Identifies highly frustrated cycles as key to effective clamping.

Provides empirical guidelines for practitioners.

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.