  We propose a method for improving approximate inference methods that corrects
for the influence of loops in the graphical model. The method is applicable to
arbitrary factor graphs, provided that the size of the Markov blankets is not
too large. It is an alternative implementation of an idea introduced recently
by Montanari and Rizzo (2005). In its simplest form, which amounts to the
assumption that no loops are present, the method reduces to the minimal Cluster
Variation Method approximation (which uses maximal factors as outer clusters).
On the other hand, using estimates of the effect of loops (obtained by some
approximate inference algorithm) and applying the Loop Correcting (LC) method
usually gives significantly better results than applying the approximate
inference algorithm directly without loop corrections. Indeed, we often observe
that the loop corrected error is approximately the square of the error of the
approximate inference method used to estimate the effect of loops. We compare
different variants of the Loop Correcting method with other approximate
inference methods on a variety of graphical models, including "real world"
networks, and conclude that the LC approach generally obtains the most accurate
results.
