A Remark on the Lasso and the Dantzig Selector

Yohann de Castro (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Domaines: Théorie de l'information et codage [math.IT]; Théorie de l'information [cs.IT]; Théorie [stat.TH]

Yohann de Castro. A Remark on the Lasso and the Dantzig Selector. Statistics and Probability Letters, 2013, 83 (1), pp.Pages 304-314. ⟨hal-00678421⟩