A Remark on the Lasso and the Dantzig Selector

Yohann de Castro

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arXiv · 1108.5533

A Remark on the Lasso and the Dantzig Selector

Yohann de Castro

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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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Yohann de Castro. 2012-09-28. A Remark on the Lasso and the Dantzig Selector. https://arxiv.org/abs/1108.5533

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