Abstract
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 language | English |
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Title of host publication | NIPS 2006 |
Subtitle of host publication | Proceedings of the 19th International Conference on Neural Information Processing Systems |
Editors | Bernhard Scholkopf, John C. Platt, Thomas Hofmann |
Publisher | MIT Press Journals |
Pages | 369-376 |
Number of pages | 8 |
ISBN (Electronic) | 0262195682, 9780262195683 |
State | Published - 2006 |
Externally published | Yes |
Event | 19th International Conference on Neural Information Processing Systems, NIPS 2006 - Vancouver, Canada Duration: 4 Dec 2006 → 7 Dec 2006 |
Publication series
Name | NIPS 2006: Proceedings of the 19th International Conference on Neural Information Processing Systems |
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Conference
Conference | 19th International Conference on Neural Information Processing Systems, NIPS 2006 |
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Country/Territory | Canada |
City | Vancouver |
Period | 4/12/06 → 7/12/06 |
Bibliographical note
Publisher Copyright:© NIPS 2006.All rights reserved