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L1-based relaxations for sparsity recovery and graphical model selection in the high-dimensional regime

Published on Feb 25, 20076268 Views

The problem of estimating a sparse signal embedded in noise arises in various contexts, including signal denoising and approximation, as well as graphical model selection. The natural optimization-the

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Chapter list

L1 regularization in the high-dimensional setting:<br> Thresholds for sparsity recovery and model selection00:05
Introduction00:46
Subset selection in regression02:23
Illustration: Reconstruction in overcomplete bases04:34
Graphical model selection06:31
Sparsity recovery with `1 relaxations08:18
Partial overview of previous work10:41
Problem formulation12:52
Assumptions on random Gaussian ensembles15:02
Illustrative examples16:36
Covariance § versus random matrix17:29
Thresholds for linear regression18:12
Illustration: Uniform Gaussian ensemble19:29
Some corollaries20:18
Graphical model selection21:55
Method and notation24:09
Assumptions25:41
Model selection via regression26:18
Summary and future directions28:07