A remark on the lasso and the Dantzig selector

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• 作者：Yohann de Castro¹ ; ^{yohann.decastro@gmail.com} ; ^{yohann.decastro@math.u-psud.fr}
• 关键词：Lasso ; Dantzig selector ; Oracle inequality ; Almost-Euclidean section ; Distortion
• 刊名：Statistics and Probability Letters
• 出版年：2013
• 出版时间：January, 2013
• 年：2013
• 卷：83
• 期：1
• 页码：304-314
• 全文大小：254 K

文摘

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.