  Belief Propagation (BP) is one of the most popular methods for inference in
probabilistic graphical models. BP is guaranteed to return the correct answer
for tree structures, but can be incorrect or non-convergent for loopy graphical
models. Recently, several new approximate inference algorithms based on cavity
distribution have been proposed. These methods can account for the effect of
loops by incorporating the dependency between BP messages. Alternatively,
region-based approximations (that lead to methods such as Generalized Belief
Propagation) improve upon BP by considering interactions within small clusters
of variables, thus taking small loops within these clusters into account. This
paper introduces an approach, Generalized Loop Correction (GLC), that benefits
from both of these types of loop correction. We show how GLC relates to these
two families of inference methods, then provide empirical evidence that GLC
works effectively in general, and can be significantly more accurate than both
correction schemes.
