Information-Theoretic Limits on Sparsity Recovery in the High-Dimensional and Noisy Setting

The problem of sparsity pattern or support set recovery refers to estimating the set of nonzero coefficients of an unknown vector beta* isin Ropf p based on a set of n noisy observations. It arises in a variety of settings, including subset selection in regression, graphical model selection, signal...

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Vydáno v:	IEEE transactions on information theory Ročník 55; číslo 12; s. 5728 - 5741
Hlavní autor:	Wainwright, M.J.
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	New York, NY IEEE 01.12.2009 Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:	Applied sciences Beta Coding, codes Complexity Compressed sensing Computational complexity Decoders Decoding Detection, estimation, filtering, equalization, prediction ell_1 -relaxation Estimating techniques Exact sciences and technology Fano's method Gaussian noise Graphical models high-dimensional statistical inference Information theory Information, signal and communications theory information-theoretic bounds Lasso Mathematical analysis Mathematical models Matrices Matrix Matrix methods Measurement Miscellaneous model selection Particle measurements Polynomials Quadratic programming Recovery Sample size Signal and communications theory Signal denoising Signal processing Signal, noise Size measurement sparsity pattern sparsity recovery subset selection Sufficient conditions support recovery Telecommunications and information theory Parameter estimation Noise reduction Lasso Polynomial method information-theoretic bounds Linear model Relaxation ℓ Fano's method subset selection Model selection Decoding Quadratic programming Signal denoising Computational complexity Polynomial time sparsity recovery Selection problem Necessary condition Sufficient condition Regression model Signal processing sparsity pattern support recovery Compressed sensing high-dimensional statistical inference Information theory
ISSN:	0018-9448, 1557-9654
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