### Abstract

A class of Maximum A Posteriori(MAP) formulations built on various graph models are of great interests for both theoretical and practical applications. Recent advances in this field have extended the connections between the linear program (LP) relaxation and various tree-reweighted message passing algorithms. At both sides, many algorithms and their optimality certificates are proved, provided no conflict exists between the node marginal maximum and the corresponding edge marginal maximum. However, these conflicts are usually inevitable for general non-trivial Markov random fields (MRFs). Our work is aimed at reducing such conflicts by reparameterizing the original energy distributions in pairwise Markov random field. All node potentials will be decomposed and attached to local edges according to their local graph structures. And thus, only edge marginals are needed in our linear program relaxation, and the node marginals are only used to exchange information among different parts of the graph. We incorporated this consistent graph-structured reparameterization into some latest LP optimality guaranteed proximal solvers, and the resulted algorithms outperform the original ones in convergence rate and also have a better behavior to converge to MAP optimality monotonously even for some highly noisy MRFs.

Original language | English |
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Title of host publication | APPLIED COMPUTING 2010 - The 25th Annual ACM Symposium on Applied Computing |

Pages | 974-978 |

Number of pages | 5 |

DOIs | |

State | Published - 23 Jul 2010 |

Event | 25th Annual ACM Symposium on Applied Computing, SAC 2010 - Sierre, Switzerland Duration: 22 Mar 2010 → 26 Mar 2010 |

### Publication series

Name | Proceedings of the ACM Symposium on Applied Computing |
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### Conference

Conference | 25th Annual ACM Symposium on Applied Computing, SAC 2010 |
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Country | Switzerland |

City | Sierre |

Period | 22/03/10 → 26/03/10 |

### Fingerprint

### Keywords

- MAP optimality
- Markov random field
- linear program

### Cite this

*APPLIED COMPUTING 2010 - The 25th Annual ACM Symposium on Applied Computing*(pp. 974-978). (Proceedings of the ACM Symposium on Applied Computing). https://doi.org/10.1145/1774088.1774291

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*APPLIED COMPUTING 2010 - The 25th Annual ACM Symposium on Applied Computing.*Proceedings of the ACM Symposium on Applied Computing, pp. 974-978, 25th Annual ACM Symposium on Applied Computing, SAC 2010, Sierre, Switzerland, 22/03/10. https://doi.org/10.1145/1774088.1774291

**Reparameterization based consistent graph-structured linear programs.** / Zhou, Hongbo; Cheng, Qiang; She, Zhikun.

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

TY - GEN

T1 - Reparameterization based consistent graph-structured linear programs

AU - Zhou, Hongbo

AU - Cheng, Qiang

AU - She, Zhikun

PY - 2010/7/23

Y1 - 2010/7/23

N2 - A class of Maximum A Posteriori(MAP) formulations built on various graph models are of great interests for both theoretical and practical applications. Recent advances in this field have extended the connections between the linear program (LP) relaxation and various tree-reweighted message passing algorithms. At both sides, many algorithms and their optimality certificates are proved, provided no conflict exists between the node marginal maximum and the corresponding edge marginal maximum. However, these conflicts are usually inevitable for general non-trivial Markov random fields (MRFs). Our work is aimed at reducing such conflicts by reparameterizing the original energy distributions in pairwise Markov random field. All node potentials will be decomposed and attached to local edges according to their local graph structures. And thus, only edge marginals are needed in our linear program relaxation, and the node marginals are only used to exchange information among different parts of the graph. We incorporated this consistent graph-structured reparameterization into some latest LP optimality guaranteed proximal solvers, and the resulted algorithms outperform the original ones in convergence rate and also have a better behavior to converge to MAP optimality monotonously even for some highly noisy MRFs.

AB - A class of Maximum A Posteriori(MAP) formulations built on various graph models are of great interests for both theoretical and practical applications. Recent advances in this field have extended the connections between the linear program (LP) relaxation and various tree-reweighted message passing algorithms. At both sides, many algorithms and their optimality certificates are proved, provided no conflict exists between the node marginal maximum and the corresponding edge marginal maximum. However, these conflicts are usually inevitable for general non-trivial Markov random fields (MRFs). Our work is aimed at reducing such conflicts by reparameterizing the original energy distributions in pairwise Markov random field. All node potentials will be decomposed and attached to local edges according to their local graph structures. And thus, only edge marginals are needed in our linear program relaxation, and the node marginals are only used to exchange information among different parts of the graph. We incorporated this consistent graph-structured reparameterization into some latest LP optimality guaranteed proximal solvers, and the resulted algorithms outperform the original ones in convergence rate and also have a better behavior to converge to MAP optimality monotonously even for some highly noisy MRFs.

KW - MAP optimality

KW - Markov random field

KW - linear program

UR - http://www.scopus.com/inward/record.url?scp=77954748925&partnerID=8YFLogxK

U2 - 10.1145/1774088.1774291

DO - 10.1145/1774088.1774291

M3 - Conference contribution

AN - SCOPUS:77954748925

SN - 9781605586380

T3 - Proceedings of the ACM Symposium on Applied Computing

SP - 974

EP - 978

BT - APPLIED COMPUTING 2010 - The 25th Annual ACM Symposium on Applied Computing

ER -