Belief Propagation for Linear Programming
| Autor: | Jinwoo Shin, Andrew E. Gelfand, Michael Chertkov |
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| Rok vydání: | 2013 |
| Předmět: |
FOS: Computer and information sciences
Sequence Mathematical optimization Linear programming Matching (graph theory) Computer Science - Artificial Intelligence Iterative method Heuristic Belief propagation Linear programming relaxation Artificial Intelligence (cs.AI) Computer Science - Data Structures and Algorithms Applied mathematics Data Structures and Algorithms (cs.DS) Cutting-plane method Mathematics |
| Zdroj: | ISIT |
| DOI: | 10.1109/isit.2013.6620626 |
| Popis: | Belief Propagation (BP) is a popular, distributed heuristic for performing MAP computations in Graphical Models. BP can be interpreted, from a variational perspective, as minimizing the Bethe Free Energy (BFE). BP can also be used to solve a special class of Linear Programming (LP) problems. For this class of problems, MAP inference can be stated as an integer LP with an LP relaxation that coincides with minimization of the BFE at ``zero temperature". We generalize these prior results and establish a tight characterization of the LP problems that can be formulated as an equivalent LP relaxation of MAP inference. Moreover, we suggest an efficient, iterative annealing BP algorithm for solving this broader class of LP problems. We demonstrate the algorithm's performance on a set of weighted matching problems by using it as a cutting plane method to solve a sequence of LPs tightened by adding ``blossom'' inequalities. To appear in ISIT 2013 |
| Databáze: | OpenAIRE |
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