Belief propagation for linear programming

Conference Paper

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. © 2013 IEEE.

Full Text

Duke Authors

Cited Authors

  • Gelfand, AE; Shin, J; Chertkov, M

Published Date

  • December 19, 2013

Published In

Start / End Page

  • 2249 - 2253

International Standard Serial Number (ISSN)

  • 2157-8095

International Standard Book Number 13 (ISBN-13)

  • 9781479904464

Digital Object Identifier (DOI)

  • 10.1109/ISIT.2013.6620626

Citation Source

  • Scopus