Using combinatorial optimization within max-product belief propagation

John Duchi*, Daniel Tarlow, Gal Elidan, Daphne Koller

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

37 Scopus citations


In general, the problem of computing a maximum a posteriori (MAP) assignment in a Markov random field (MRF) is computationally intractable. However, in certain subclasses of MRF, an optimal or close-to-optimal assignment can be found very efficiently using combinatorial optimization algorithms: certain MRFs with mutual exclusion constraints can be solved using bipartite matching, and MRFs with regular potentials can be solved using minimum cut methods. However, these solutions do not apply to the many MRFs that contain such tractable components as sub-networks, but also other non-complying potentials. In this paper, we present a new method, called COMPOSE, for exploiting combinatorial optimization for sub-networks within the context of a max-product belief propagation algorithm. COMPOSE uses combinatorial optimization for computing exact max-marginals for an entire sub-network; these can then be used for inference in the context of the network as a whole. We describe highly efficient methods for computing max-marginals for subnetworks corresponding both to bipartite matchings and to regular networks. We present results on both synthetic and real networks encoding correspondence problems between images, which involve both matching constraints and pairwise geometric constraints. We compare to a range of current methods, showing that the ability of COMPOSE to transmit information globally across the network leads to improved convergence, decreased running time, and higher-scoring assignments.

Original languageAmerican English
Title of host publicationAdvances in Neural Information Processing Systems 19 - Proceedings of the 2006 Conference
Number of pages8
StatePublished - 2007
Externally publishedYes
Event20th Annual Conference on Neural Information Processing Systems, NIPS 2006 - Vancouver, BC, Canada
Duration: 4 Dec 20067 Dec 2006

Publication series

NameAdvances in Neural Information Processing Systems
ISSN (Print)1049-5258


Conference20th Annual Conference on Neural Information Processing Systems, NIPS 2006
CityVancouver, BC


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