Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation

Computingmaximum a posteriori (MAP) estimation in graphical models is an important inference problem with many applications. We present message-passing algorithms for quadratic programming (QP) formulations of MAP estimation for pairwise Markov random fields. In particular, we use the concaveconvex procedure (CCCP) to obtain a locally optimal algorithm for the non-convex QP formulation. A similar technique is used to derive a globally convergent algorithm for the convex QP relaxation of MAP. We also show that a recently developed expectationmaximization (EM) algorithm for the QP formulation of MAP can be derived from the CCCP perspective. Experiments on synthetic and real-world problems confirm that our new approach is competitive with maxproduct and its variations. Compared with CPLEX, we achieve more than an order-ofmagnitude speedup in solving optimally the convex QP relaxation.