TY - GEN

T1 - Clusters and coarse partitions in LP relaxations

AU - Sontag, David

AU - Globerson, Amir

AU - Jaakkola, Tommi

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

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M3 - Conference contribution

AN - SCOPUS:80053168886

SN - 9781605609492

T3 - Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference

SP - 1537

EP - 1544

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

T2 - 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008

Y2 - 8 December 2008 through 11 December 2008

ER -