Finding the M most probable configurations using loopy belief propagation

Loopy belief propagation (BP) has been successfully used in a num- ber of difficult graphical models to find the most probable configu- ration 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 prob- lems the clique size in the junction tree is prohibitively large. In this work we address the problem of finding the M best configura- Tions when exact inference is impossible. We start by developing a new exact inference algorithm for calculat- ing the best configurations that uses only max-marginals. For ap- proximate inference, we replace the max-marginals with the beliefs calculated using max-product BP and generalized BP.We show em-pirically that the algorithm can accurately and rapidly approximate the M best configurations in graphs with hundreds of variables.