S-AMP for non-linear observation models

Burak Cakmak; Ole Winther; Bernard H. Fleury

doi:10.1109/ISIT.2015.7282968

S-AMP for non-linear observation models

Burak Cakmak
, Ole Winther
, Bernard H. Fleury

Aalborg University

Research output: Chapter in Book/Report/Conference proceeding › Article in proceedings › Research › peer-review

Abstract

Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation-propagation-(EP)-like equations from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.

Original language	English
Title of host publication	Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT)
Publisher	IEEE
Publication date	2015
Pages	2807-2811
ISBN (Print)	978-1-4673-7704-1
DOIs	https://doi.org/10.1109/ISIT.2015.7282968
Publication status	Published - 2015
Event	2015 IEEE International Symposium on Information Theory - Hong Kong, Hong Kong Duration: 14 Jun 2015 → 19 Jun 2015 http://www.isit2015.org/

Conference

Conference	2015 IEEE International Symposium on Information Theory
Country/Territory	Hong Kong
City	Hong Kong
Period	14/06/2015 → 19/06/2015
Internet address	http://www.isit2015.org/

Keywords

Approximate Message Passing
Expectation Propagation
Free Probability
Variational Inference

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title = "S-AMP for non-linear observation models",

abstract = "Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation-propagation-(EP)-like equations from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.",

keywords = "Approximate Message Passing, Expectation Propagation, Free Probability, Variational Inference",

author = "Burak Cakmak and Ole Winther and Fleury, \{Bernard H.\}",

year = "2015",

doi = "10.1109/ISIT.2015.7282968",

language = "English",

isbn = "978-1-4673-7704-1",

pages = "2807--2811",

booktitle = "Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT)",

publisher = "IEEE",

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note = "2015 IEEE International Symposium on Information Theory, ISIT 2015 ; Conference date: 14-06-2015 Through 19-06-2015",

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TY - GEN

T1 - S-AMP for non-linear observation models

AU - Cakmak, Burak

AU - Winther, Ole

AU - Fleury, Bernard H.

PY - 2015

Y1 - 2015

N2 - Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation-propagation-(EP)-like equations from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.

AB - Recently we presented the S-AMP approach, an extension of approximate message passing (AMP), to be able to handle general invariant matrix ensembles. In this contribution we extend S-AMP to non-linear observation models. We obtain generalized AMP (GAMP) as the special case when the measurement matrix has zero-mean iid Gaussian entries. Our derivation is based upon 1) deriving expectation-propagation-(EP)-like equations from the stationary-points equations of the Gibbs free energy under first- and second-moment constraints and 2) applying additive free convolution in free probability theory to get low-complexity updates for the second moment quantities.

KW - Approximate Message Passing

KW - Expectation Propagation

KW - Free Probability

KW - Variational Inference

U2 - 10.1109/ISIT.2015.7282968

DO - 10.1109/ISIT.2015.7282968

M3 - Article in proceedings

SN - 978-1-4673-7704-1

SP - 2807

EP - 2811

BT - Proceedings of the 2015 IEEE International Symposium on Information Theory (ISIT)

PB - IEEE

T2 - 2015 IEEE International Symposium on Information Theory

Y2 - 14 June 2015 through 19 June 2015

ER -

S-AMP for non-linear observation models

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Keywords

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