An LP view of the M-best MAP problem

Menachem Fromer, Amir Globerson

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

Abstract

We consider the problem of finding the M assignments with maximum probability in a probabilistic graphical model. We show how this problem can be formulated as a linear program (LP) on a particular polytope. We prove that, for tree graphs (and junction trees in general), this polytope has a particularly simple form and differs from the marginal polytope in a single inequality constraint. We use this characterization to provide an approximation scheme for non-tree graphs, by using the set of spanning trees over such graphs. The method we present puts the M-best inference problem in the context of LP relaxations, which have recently received considerable attention and have proven useful in solving difficult inference problems. We show empirically that our method often finds the provably exact M best configurations for problems of high tree-width.

Original languageEnglish
Title of host publicationAdvances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference
Pages567-575
Number of pages9
StatePublished - 2009
Externally publishedYes
Event23rd Annual Conference on Neural Information Processing Systems, NIPS 2009 - Vancouver, BC, Canada
Duration: 7 Dec 200910 Dec 2009

Publication series

NameAdvances in Neural Information Processing Systems 22 - Proceedings of the 2009 Conference

Conference

Conference23rd Annual Conference on Neural Information Processing Systems, NIPS 2009
Country/TerritoryCanada
CityVancouver, BC
Period7/12/0910/12/09

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