### Abstract

Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper summarizes a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with each weak edge representing a small, linearizable coupling of variables. AMP approximations based on the central limit theorem can be applied to the weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (Hybrid-GAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition between strong and weak edges, a performance-complexity trade-off can be achieved. Structured sparsity problems are studied as an example of this general methodology where there is a natural partition of edges.

Original language | English (US) |
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Title of host publication | 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012 |

Pages | 1236-1240 |

Number of pages | 5 |

DOIs | |

State | Published - 2012 |

Event | 2012 IEEE International Symposium on Information Theory, ISIT 2012 - Cambridge, MA, United States Duration: Jul 1 2012 → Jul 6 2012 |

### Other

Other | 2012 IEEE International Symposium on Information Theory, ISIT 2012 |
---|---|

Country | United States |

City | Cambridge, MA |

Period | 7/1/12 → 7/6/12 |

### Fingerprint

### ASJC Scopus subject areas

- Applied Mathematics
- Modeling and Simulation
- Theoretical Computer Science
- Information Systems

### Cite this

*2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012*(pp. 1236-1240). [6283054] https://doi.org/10.1109/ISIT.2012.6283054

**Hybrid generalized approximate message passing with applications to structured sparsity.** / Rangan, Sundeep; Fletcher, Alyson K.; Goyal, Vivek K.; Schniter, Philip.

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

*2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012.*, 6283054, pp. 1236-1240, 2012 IEEE International Symposium on Information Theory, ISIT 2012, Cambridge, MA, United States, 7/1/12. https://doi.org/10.1109/ISIT.2012.6283054

}

TY - GEN

T1 - Hybrid generalized approximate message passing with applications to structured sparsity

AU - Rangan, Sundeep

AU - Fletcher, Alyson K.

AU - Goyal, Vivek K.

AU - Schniter, Philip

PY - 2012

Y1 - 2012

N2 - Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper summarizes a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with each weak edge representing a small, linearizable coupling of variables. AMP approximations based on the central limit theorem can be applied to the weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (Hybrid-GAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition between strong and weak edges, a performance-complexity trade-off can be achieved. Structured sparsity problems are studied as an example of this general methodology where there is a natural partition of edges.

AB - Gaussian and quadratic approximations of message passing algorithms on graphs have attracted considerable attention due to their computational simplicity, analytic tractability, and wide applicability in optimization and statistical inference problems. This paper summarizes a systematic framework for incorporating such approximate message passing (AMP) methods in general graphical models. The key concept is a partition of dependencies of a general graphical model into strong and weak edges, with each weak edge representing a small, linearizable coupling of variables. AMP approximations based on the central limit theorem can be applied to the weak edges and integrated with standard message passing updates on the strong edges. The resulting algorithm, which we call hybrid generalized approximate message passing (Hybrid-GAMP), can yield significantly simpler implementations of sum-product and max-sum loopy belief propagation. By varying the partition between strong and weak edges, a performance-complexity trade-off can be achieved. Structured sparsity problems are studied as an example of this general methodology where there is a natural partition of edges.

UR - http://www.scopus.com/inward/record.url?scp=84867515003&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84867515003&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2012.6283054

DO - 10.1109/ISIT.2012.6283054

M3 - Conference contribution

AN - SCOPUS:84867515003

SN - 9781467325790

SP - 1236

EP - 1240

BT - 2012 IEEE International Symposium on Information Theory Proceedings, ISIT 2012

ER -