Clusters and coarse partitions in LP relaxations

David Sontag, Amir Globerson, Tommi Jaakkola

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We propose a new class of consistency constraints for Linear Programming (LP) relaxations for finding the most probable (MAP) configuration in graphical models. Usual cluster-based LP relaxations enforce joint consistency on the beliefs of a cluster of variables, with computational cost increasing exponentially with the size of the clusters. By partitioning the state space of a cluster and enforcing consistency only across partitions, we obtain a class of constraints which, although less tight, are computationally feasible for large clusters. We show how to solve the cluster selection and partitioning problem monotonically in the dual LP, using the current beliefs to guide these choices. We obtain a dual message passing algorithm and apply it to protein design problems where the variables have large state spaces and the usual cluster-based relaxations are very costly. The resulting method solves many of these problems exactly, and significantly faster than a method that does not use partitioning.

Original languageEnglish (US)
Title of host publicationAdvances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference
Pages1537-1544
Number of pages8
StatePublished - 2009
Event22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 - Vancouver, BC, Canada
Duration: Dec 8 2008Dec 11 2008

Publication series

NameAdvances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference

Other

Other22nd Annual Conference on Neural Information Processing Systems, NIPS 2008
CountryCanada
CityVancouver, BC
Period12/8/0812/11/08

ASJC Scopus subject areas

  • Information Systems

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    Sontag, D., Globerson, A., & Jaakkola, T. (2009). Clusters and coarse partitions in LP relaxations. In Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference (pp. 1537-1544). (Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference).