A Practical Scheme and Fast Algorithm to Tune the Lasso With Optimality Guarantees

Michael Chichignoud; Johannes Lederer; Martin J. Wainwright

We introduce a novel scheme for choosing the regularization parameter in high-dimensional linear regression with Lasso. This scheme, inspired by Lepskiâs method for bandwidth selection in non-parametric regression, is equipped with both optimal finite-sample guarantees and a fast algorithm. In particular, for any design matrix such that the Lasso has low sup-norm error under an âoracle choiceâ of the regularization parameter, we show that our method matches the oracle performance up to a small constant factor, and show that it can be implemented by performing simple tests along a single Lasso path. By applying the Lasso to simulated and real data, we find that our novel scheme can be faster and more accurate than standard schemes such as Cross-Validation.

A Practical Scheme and Fast Algorithm to Tune the Lasso With Optimality Guarantees

Abstract