Message Passing Algorithms for MAP Estimation using DC Programming
We address the problem of finding the most likely assignment or MAP estimation in a Markov random field. We analyze the linear programming formulation of MAP through the lens of difference of convex functions (DC) programming, and use the concave-convex procedure (CCCP) to develop efficient message-...
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| Main Authors: | , , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2012
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| Online Access: | https://ink.library.smu.edu.sg/sis_research/2203 https://ink.library.smu.edu.sg/context/sis_research/article/3203/viewcontent/Message_Passing_Algorithms_for_MAP_Estimation_Using_DC_Programming.pdf |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | We address the problem of finding the most likely assignment or MAP estimation in a Markov random field. We analyze the linear programming formulation of MAP through the lens of difference of convex functions (DC) programming, and use the concave-convex procedure (CCCP) to develop efficient message-passing solvers. The resulting algorithms are guaranteed to converge to a global optimum of the well-studied local polytope, an outer bound on the MAP marginal polytope. To tighten the outer bound, we show how to combine it with the mean-field based inner bound and, again, solve it using CCCP. We also identify a useful relationship between the DC formulations and some recently proposed algorithms based on Bregman divergence. Experimentally, this hybrid approach produces optimal solutions for a range of hard OR problems and nearoptimal solutions for standard benchmarks. |
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