A Remark on the Lasso and the Dantzig Selector
Statistics Theory
2012-10-01 v3 Information Theory
Functional Analysis
math.IT
Statistics Theory
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.
Cite
@article{arxiv.1108.5533,
title = {A Remark on the Lasso and the Dantzig Selector},
author = {Yohann de Castro},
journal= {arXiv preprint arXiv:1108.5533},
year = {2012}
}
Comments
Final Version. This article was written mostly during his Ph.D. at the Institut de Math\'ematiques de Toulouse (IMT)