Tuning Lasso for sup-norm optimality, Michaël Chichignoud, Johannes Lederer, Martin Wainwright, 10-1-14

Tuning Lasso for sup-norm optimality

Michaël Chichignoud, Johannes Lederer, Martin Wainwright(Submitted on 1 Oct 2014)

We introduce novel schemes for tuning parameter calibration in high-dimensional linear regression with Lasso. These calibration schemes are inspired by Lepski's method for bandwidth adaptation in non-parametric regression and are the first calibration schemes that are equipped with both theoretical guarantees and fast algorithms. In particular, we develop optimal finite sample guarantees for sup-norm performance and give algorithms that consist of simple tests along a single Lasso path. Moreover, we show that false positives can be safely reduced without increasing the number of false negatives. Applying Lasso to synthetic data and to real data, we finally demonstrate that the novel schemes can rival standard schemes such as Cross-Validation in speed as well as in sup-norm and variable selection performance.

Subjects: Methodology (stat.ME); Statistics Theory (math.ST)Cite as: arXiv:1410.0247 [stat.ME]  (or arXiv:1410.0247v1 [stat.ME] for this version)