A Remark on the Lasso and the Dantzig Selector

2011/08/29 by de Castro, Yohann
#FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Information Theory (cs.IT) #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.1108.5533

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

• Generalization of l1 constraints for high dimensional regression problems
• The degrees of freedom of the Lasso for general design matrix
• Thresholded Lasso for high dimensional variable selection
• The Complete Lasso Tradeoff Diagram
• Thresholded Lasso for high dimensional variable selection and statistical estimation