Generalized approximate message passing for estimation with random linear mixing

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We consider the estimation of a random vector observed through a linear transform followed by a componentwise probabilistic measurement channel. Although such linear mixing estimation problems are generally highly non-convex, Gaussian approximations of belief propagation (BP) have proven to be computationally attractive and highly effective in a range of applications. Recently, Bayati and Montanari have provided a rigorous and extremely general analysis of a large class of approximate message passing (AMP) algorithms that includes many Gaussian approximate BP methods. This paper extends their analysis to a larger class of algorithms to include what we call generalized AMP (G-AMP). G-AMP incorporates general (possibly non-AWGN) measurement channels. Similar to the AWGN output channel case, we show that the asymptotic behavior of the G-AMP algorithm under large i.i.d. Gaussian transform matrices is described by a simple set of state evolution (SE) equations. The general SE equations recover and extend several earlier results, including SE equations for approximate BP on general output channels by Guo and Wang.

Original languageEnglish (US)
Title of host publication2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
Pages2168-2172
Number of pages5
DOIs
StatePublished - 2011
Event2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 - St. Petersburg, Russian Federation
Duration: Jul 31 2011Aug 5 2011

Other

Other2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011
CountryRussian Federation
CitySt. Petersburg
Period7/31/118/5/11

Fingerprint

Belief Propagation
Message passing
State Equation
Message Passing
Evolution Equation
Transform
Message-passing Algorithms
Gaussian Approximation
Approximate Algorithm
Output
Random Vector
Asymptotic Behavior
Range of data
Class

Keywords

  • belief propagation
  • compressed sensing
  • estimation
  • Optimization
  • random matrices

ASJC Scopus subject areas

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

Cite this

Rangan, S. (2011). Generalized approximate message passing for estimation with random linear mixing. In 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011 (pp. 2168-2172). [6033942] https://doi.org/10.1109/ISIT.2011.6033942

Generalized approximate message passing for estimation with random linear mixing. / Rangan, Sundeep.

2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011. 2011. p. 2168-2172 6033942.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Rangan, S 2011, Generalized approximate message passing for estimation with random linear mixing. in 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011., 6033942, pp. 2168-2172, 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011, St. Petersburg, Russian Federation, 7/31/11. https://doi.org/10.1109/ISIT.2011.6033942
Rangan S. Generalized approximate message passing for estimation with random linear mixing. In 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011. 2011. p. 2168-2172. 6033942 https://doi.org/10.1109/ISIT.2011.6033942
Rangan, Sundeep. / Generalized approximate message passing for estimation with random linear mixing. 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011. 2011. pp. 2168-2172
@inproceedings{3ae817facb82400188578c5aca975cf8,
title = "Generalized approximate message passing for estimation with random linear mixing",
abstract = "We consider the estimation of a random vector observed through a linear transform followed by a componentwise probabilistic measurement channel. Although such linear mixing estimation problems are generally highly non-convex, Gaussian approximations of belief propagation (BP) have proven to be computationally attractive and highly effective in a range of applications. Recently, Bayati and Montanari have provided a rigorous and extremely general analysis of a large class of approximate message passing (AMP) algorithms that includes many Gaussian approximate BP methods. This paper extends their analysis to a larger class of algorithms to include what we call generalized AMP (G-AMP). G-AMP incorporates general (possibly non-AWGN) measurement channels. Similar to the AWGN output channel case, we show that the asymptotic behavior of the G-AMP algorithm under large i.i.d. Gaussian transform matrices is described by a simple set of state evolution (SE) equations. The general SE equations recover and extend several earlier results, including SE equations for approximate BP on general output channels by Guo and Wang.",
keywords = "belief propagation, compressed sensing, estimation, Optimization, random matrices",
author = "Sundeep Rangan",
year = "2011",
doi = "10.1109/ISIT.2011.6033942",
language = "English (US)",
isbn = "9781457705953",
pages = "2168--2172",
booktitle = "2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011",

}

TY - GEN

T1 - Generalized approximate message passing for estimation with random linear mixing

AU - Rangan, Sundeep

PY - 2011

Y1 - 2011

N2 - We consider the estimation of a random vector observed through a linear transform followed by a componentwise probabilistic measurement channel. Although such linear mixing estimation problems are generally highly non-convex, Gaussian approximations of belief propagation (BP) have proven to be computationally attractive and highly effective in a range of applications. Recently, Bayati and Montanari have provided a rigorous and extremely general analysis of a large class of approximate message passing (AMP) algorithms that includes many Gaussian approximate BP methods. This paper extends their analysis to a larger class of algorithms to include what we call generalized AMP (G-AMP). G-AMP incorporates general (possibly non-AWGN) measurement channels. Similar to the AWGN output channel case, we show that the asymptotic behavior of the G-AMP algorithm under large i.i.d. Gaussian transform matrices is described by a simple set of state evolution (SE) equations. The general SE equations recover and extend several earlier results, including SE equations for approximate BP on general output channels by Guo and Wang.

AB - We consider the estimation of a random vector observed through a linear transform followed by a componentwise probabilistic measurement channel. Although such linear mixing estimation problems are generally highly non-convex, Gaussian approximations of belief propagation (BP) have proven to be computationally attractive and highly effective in a range of applications. Recently, Bayati and Montanari have provided a rigorous and extremely general analysis of a large class of approximate message passing (AMP) algorithms that includes many Gaussian approximate BP methods. This paper extends their analysis to a larger class of algorithms to include what we call generalized AMP (G-AMP). G-AMP incorporates general (possibly non-AWGN) measurement channels. Similar to the AWGN output channel case, we show that the asymptotic behavior of the G-AMP algorithm under large i.i.d. Gaussian transform matrices is described by a simple set of state evolution (SE) equations. The general SE equations recover and extend several earlier results, including SE equations for approximate BP on general output channels by Guo and Wang.

KW - belief propagation

KW - compressed sensing

KW - estimation

KW - Optimization

KW - random matrices

UR - http://www.scopus.com/inward/record.url?scp=80054799706&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80054799706&partnerID=8YFLogxK

U2 - 10.1109/ISIT.2011.6033942

DO - 10.1109/ISIT.2011.6033942

M3 - Conference contribution

SN - 9781457705953

SP - 2168

EP - 2172

BT - 2011 IEEE International Symposium on Information Theory Proceedings, ISIT 2011

ER -