Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation

摘要

Computing maximum a posteriori (MAP) es timation 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 concave convex procedure (CCCP) to obtain a lo cally 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 expectation maximization (EM) algorithm for the QP for mulation of MAP can be derived from the CCCP perspective. Experiments on syn thetic and real-world problems confirm that our new approach is competitive with max product and its variations. Compared with CPLEX, we achieve more than an order-of-magnitude speedup in solving optimally the convex QP relaxation.