Adaptive Damping and Mean Removal for the Generalized Approximate Message Passing Algorithm

The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of \(x\) observed from a noisy version of the transform coefficients \(z = Ax\). In fact, for large zero-mean i.i.d sub-Gaussian \(A\), GAMP is characterized by a state evolution...

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Bibliographic Details
Published in:	arXiv.org
Main Authors:	Vila, Jeremy, Schniter, Philip, Rangan, Sundeep, Krzakala, Florent, Zdeborova, Lenka
Format:	Paper
Language:	English
Published:	Ithaca Cornell University Library, arXiv.org 05.12.2014
Subjects:	Algorithms Conditioning Damping Divergence Message passing Robustness (mathematics)
ISSN:	2331-8422
Online Access:	Get full text
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Summary:	The generalized approximate message passing (GAMP) algorithm is an efficient method of MAP or approximate-MMSE estimation of \(x\) observed from a noisy version of the transform coefficients \(z = Ax\). In fact, for large zero-mean i.i.d sub-Gaussian \(A\), GAMP is characterized by a state evolution whose fixed points, when unique, are optimal. For generic \(A\), however, GAMP may diverge. In this paper, we propose adaptive damping and mean-removal strategies that aim to prevent divergence. Numerical results demonstrate significantly enhanced robustness to non-zero-mean, rank-deficient, column-correlated, and ill-conditioned \(A\).
Bibliography:	SourceType-Working Papers-1 ObjectType-Working Paper/Pre-Print-1 content type line 50
ISSN:	2331-8422
DOI:	10.48550/arxiv.1412.2005