A Practical Scheme and Fast Algorithm to Tune the Lasso with Optimality Guarantees
Abstract
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.
Cite
Text
Chichignoud et al. "A Practical Scheme and Fast Algorithm to Tune the Lasso with Optimality Guarantees." Journal of Machine Learning Research, 2016.Markdown
[Chichignoud et al. "A Practical Scheme and Fast Algorithm to Tune the Lasso with Optimality Guarantees." Journal of Machine Learning Research, 2016.](https://mlanthology.org/jmlr/2016/chichignoud2016jmlr-practical/)BibTeX
@article{chichignoud2016jmlr-practical,
title = {{A Practical Scheme and Fast Algorithm to Tune the Lasso with Optimality Guarantees}},
author = {Chichignoud, Michael and Lederer, Johannes and Wainwright, Martin J.},
journal = {Journal of Machine Learning Research},
year = {2016},
pages = {1-20},
volume = {17},
url = {https://mlanthology.org/jmlr/2016/chichignoud2016jmlr-practical/}
}