Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1152072 | Statistics & Probability Letters | 2013 | 11 Pages |
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.
Related Topics
Physical Sciences and Engineering
Mathematics
Statistics and Probability
Authors
Yohann de Castro,