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2014 Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression
Shiqing Wang, Yan Shi, Limin Su
J. Appl. Math. 2014: 1-7 (2014). DOI: 10.1155/2014/946241

Abstract

Regularity conditions play a pivotal role for sparse recovery in high-dimensional regression. In this paper, we present a weaker regularity condition and further discuss the relationships with other regularity conditions, such as restricted eigenvalue condition. We study the behavior of our new condition for design matrices with independent random columns uniformly drawn on the unit sphere. Moreover, the present paper shows that, under a sparsity scenario, the Lasso estimator and Dantzig selector exhibit similar behavior. Based on both methods, we derive, in parallel, more precise bounds for the estimation loss and the prediction risk in the linear regression model when the number of variables can be much larger than the sample size.

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Shiqing Wang. Yan Shi. Limin Su. "Weaker Regularity Conditions and Sparse Recovery in High-Dimensional Regression." J. Appl. Math. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/946241

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07132003
MathSciNet: MR3240642
Digital Object Identifier: 10.1155/2014/946241

Rights: Copyright © 2014 Hindawi

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