Conference Proceeding Article
Computing maximum 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 concave-convex 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 expectation-maximization (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 max-product and its variations. Compared with CPLEX, we achieve more than an order-of-magnitude speedup in solving optimally the convex QP relaxation.
Artificial Intelligence and Robotics | Operations Research, Systems Engineering and Industrial Engineering
Intelligent Systems and Decision Analytics
Proceedings of the 15th International Conference on Artificial Intelligence and Statistics (AISTATS) 2012, 21-23 April, La Palma, Canary Islands
Journal of Machine Learning Research
City or Country
KUMAR, Akshat and Zilberstein, Shlomo.
Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation. (2012). Proceedings of the 15th International Conference on Artificial Intelligence and Statistics (AISTATS) 2012, 21-23 April, La Palma, Canary Islands. 656-664. Research Collection School Of Information Systems.
Available at: http://ink.library.smu.edu.sg/sis_research/2205
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