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 |
|---|---|
| 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 |
|---|
Conference
| Conference | 25th Annual ACM Symposium on Applied Computing, SAC 2010 |
|---|---|
| Country | Switzerland |
| City | Sierre |
| Period | 22/03/10 → 26/03/10 |
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Keywords
- linear program
- MAP optimality
- Markov random field
Cite this
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Reparameterization based consistent graph-structured linear programs. / Zhou, Hongbo; Cheng, Qiang; She, Zhikun.
APPLIED COMPUTING 2010 - The 25th Annual ACM Symposium on Applied Computing. 2010. p. 974-978 (Proceedings of the ACM Symposium on Applied Computing).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Research › peer-review
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 - linear program
KW - MAP optimality
KW - Markov random field
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
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 -