S-AMP: Approximate Message Passing for General Matrix Ensembles

Burak  Cakmak; Ole Winther; Bernard H.  Fleury

doi:10.1109/ITW.2014.6970819

S-AMP: Approximate Message Passing for General Matrix Ensembles

Burak Cakmak
, Ole Winther
, Bernard H. Fleury

Aalborg University

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

Abstract

We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its design rather than from solving a separate optimization problem as done for AMP.

Original language	English
Title of host publication	Proceedings of 2014 IEEE Information Theory Workshop (ITW)
Publisher	IEEE
Publication date	2014
Pages	192-196
ISBN (Print)	978-1-4799-5999-0
DOIs	https://doi.org/10.1109/ITW.2014.6970819
Publication status	Published - 2014
Event	2014 IEEE Information Theory Workshop - Hobart, Australia Duration: 2 Nov 2014 → 5 Nov 2014

Workshop

Workshop	2014 IEEE Information Theory Workshop
Country/Territory	Australia
City	Hobart
Period	02/11/2014 → 05/11/2014

Keywords

Variational inference
Free energy optimization
Approximate message passing
S-transform in free probability

Access to Document

10.1109/ITW.2014.6970819

OpenUrl availability

Full text

Cite this

@inproceedings{a8e841f99b8146529dc6c179d6e12939,

title = "S-AMP: Approximate Message Passing for General Matrix Ensembles",

abstract = "We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its design rather than from solving a separate optimization problem as done for AMP.",

keywords = "Variational inference, Free energy optimization, Approximate message passing, S-transform in free probability",

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

year = "2014",

doi = "10.1109/ITW.2014.6970819",

language = "English",

isbn = "978-1-4799-5999-0",

pages = "192--196",

booktitle = "Proceedings of 2014 IEEE Information Theory Workshop (ITW)",

publisher = "IEEE",

address = "United States",

note = "2014 IEEE Information Theory Workshop, ITW2014 ; Conference date: 02-11-2014 Through 05-11-2014",

}

TY - GEN

T1 - S-AMP: Approximate Message Passing for General Matrix Ensembles

AU - Cakmak, Burak

AU - Winther, Ole

AU - Fleury, Bernard H.

PY - 2014

Y1 - 2014

N2 - We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its design rather than from solving a separate optimization problem as done for AMP.

AB - We propose a novel iterative estimation algorithm for linear observation models called S-AMP. The fixed points of S-AMP are the stationary points of the exact Gibbs free energy under a set of (first- and second-) moment consistency constraints in the large system limit. S-AMP extends the approximate message-passing (AMP) algorithm to general matrix ensembles with a well-defined large system size limit. The generalization is based on the S-transform (in free probability) of the spectrum of the measurement matrix. Furthermore, we show that the optimality of S-AMP follows directly from its design rather than from solving a separate optimization problem as done for AMP.

KW - Variational inference

KW - Free energy optimization

KW - Approximate message passing

KW - S-transform in free probability

U2 - 10.1109/ITW.2014.6970819

DO - 10.1109/ITW.2014.6970819

M3 - Article in proceedings

SN - 978-1-4799-5999-0

SP - 192

EP - 196

BT - Proceedings of 2014 IEEE Information Theory Workshop (ITW)

PB - IEEE

T2 - 2014 IEEE Information Theory Workshop

Y2 - 2 November 2014 through 5 November 2014

ER -

S-AMP: Approximate Message Passing for General Matrix Ensembles

Abstract

Workshop

Keywords

Access to Document

OpenUrl availability

Fingerprint

Cite this