Finding the M most probable configurations using loopy belief propagation

Loopy belief propagation (BP) has been successfully used in a number of difficult graphical models to find the most probable configuration of the hidden variables. In applications ranging from protein folding to image analysis one would like to find not just the best configuration but rather the top M. While this problem has been solved using the junction tree formalism, in many real world problems the clique size in the junction tree is prohibitively large. In this work we address the problem of finding the M best configurations when exact inference is impossible. We start by developing a new exact inference algorithm for calculating the best configurations that uses only max-marginals. For approximate inference, we replace the max-marginals with the beliefs, calculated using max-product BP and generalized BP. We show empirically that the algorithm can accurately and rapidly approximate the M best configurations in graphs with hundreds of variables.