Message-Passing Algorithms for Quadratic Programming Formulations of MAP Estimation
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-conve...
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2011
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| Online Access: | https://ink.library.smu.edu.sg/sis_research/2205 https://ink.library.smu.edu.sg/context/sis_research/article/3205/viewcontent/1202.3739.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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. |
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