Uncertainty in Artificial Intelligence
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Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation
Akshat Kumar, Shlomo Zilberstein
Abstract:
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.
Keywords:
Pages: 428-435
PS Link:
PDF Link: /papers/11/p428-kumar.pdf
BibTex:
@INPROCEEDINGS{Kumar11,
AUTHOR = "Akshat Kumar and Shlomo Zilberstein",
TITLE = "Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation",
BOOKTITLE = "Proceedings of the Twenty-Seventh Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-11)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2011",
PAGES = "428--435"
}


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