The LASSO Risk for Gaussian Matrices

We consider the problem of learning a coefficient vector x ο ∈ R N from noisy linear observation y = Ax o + ∈ R n . In many contexts (ranging from model selection to image processing), it is desirable to construct a sparse estimator x̂. In this case, a popular approach consists in solving an ℓ 1 -pe...

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Bibliographic Details
Published in:	IEEE transactions on information theory Vol. 58; no. 4; pp. 1997 - 2017
Main Authors:	Bayati, M., Montanari, A.
Format:	Journal Article
Language:	English
Published:	New York, NY IEEE 01.04.2012 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:	Algorithm design and analysis Applied sciences Calibration Compressed sensing Detection, estimation, filtering, equalization, prediction Equations Exact sciences and technology graphical models Image processing Image processing systems Information theory Information, signal and communications theory Mean square error methods message passing algorithms Noise Noise measurement Normal distribution random matrix theory Services and terminals of telecommunications Signal and communications theory Signal processing Signal, noise Sparsity state evolution statistical learning Systems, networks and services of telecommunications Telecommunications Telecommunications and information theory Telemetry. Remote supervision. Telewarning. Remote control Vectors state evolution Range finding statistical learning Random matrix message passing algorithms Image processing Noise reduction Model selection Least squares problem Algorithm Mean square error Learning Message passing Algorithm performance Simulation graphical models Signal processing random matrix theory Compressed sensing
ISSN:	0018-9448, 1557-9654
Online Access:	Get full text
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