A Remark on the Lasso and the Dantzig Selector

Abstract : This article investigates a new parameter for the high-dimensional regression with noise: the distortion. This latter has attracted a lot of attention recently with the appearance of new deterministic constructions of 'almost'-Euclidean sections of the L1-ball. It measures how far is the intersection between the kernel of the design matrix and the unit L1-ball from an L2-ball. We show that the distortion holds enough information to derive oracle inequalities (i.e. a comparison to an ideal situation where one knows the s largest coefficients of the target) for the lasso and the Dantzig selector.
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Contributor : Yohann de Castro <>
Submitted on : Wednesday, January 30, 2013 - 1:18:29 PM
Last modification on : Thursday, January 11, 2018 - 6:12:18 AM

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  • HAL Id : hal-00678421, version 1
  • ARXIV : 1108.5533

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Yohann de Castro. A Remark on the Lasso and the Dantzig Selector. STATISTICS & PROBABILITY LETTERS, 2013, 83 (1), pp.Pages 304-314. ⟨hal-00678421⟩

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