### 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 language | English (US) |
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Title of host publication | Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference |

Pages | 1537-1544 |

Number of pages | 8 |

State | Published - 2009 |

Event | 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 - Vancouver, BC, Canada Duration: Dec 8 2008 → Dec 11 2008 |

### Other

Other | 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008 |
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Country | Canada |

City | Vancouver, BC |

Period | 12/8/08 → 12/11/08 |

### Fingerprint

### ASJC Scopus subject areas

- Information Systems

### Cite this

*Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference*(pp. 1537-1544)

**Clusters and coarse partitions in LP relaxations.** / Sontag, David; Globerson, Amir; Jaakkola, Tommi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Advances in Neural Information Processing Systems 21 - Proceedings of the 2008 Conference.*pp. 1537-1544, 22nd Annual Conference on Neural Information Processing Systems, NIPS 2008, Vancouver, BC, Canada, 12/8/08.

}

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.

UR - http://www.scopus.com/inward/record.url?scp=80053168886&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053168886&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9781605609492

SP - 1537

EP - 1544

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

ER -