PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Clusters and Coarse Partitions in LP Relaxations
David Sontag, Amir Globerson and Tommi Jaakkola
Advances in Nerual Information Processing Systems Volume 22, 2009.


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 con- sistency 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 result- ing method solves many of these problems exactly, and significantly faster than a method that does not use partitioning.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Computational, Information-Theoretic Learning with Statistics
Theory & Algorithms
ID Code:5412
Deposited By:Amir Globerson
Deposited On:24 June 2009