Look-Ahead Screening Rules for the Lasso
The lasso is a popular method to induce shrinkage and sparsity in the solution vector (coefficients) of regression problems, particularly when there are many predictors relative to the number of observations. Solving the lasso in this high-dimensional setting can, however, be computationally demanding. Fortunately, this demand can be alleviated via the use of screening rules that discard predictors prior to fitting the model, leading to a reduced problem to be solved. In this paper, we present a new screening strategy: look-ahead screening. Our method uses safe screening rules to find a range of penalty values for which a given predictor cannot enter the model, thereby screening predictors along the remainder of the path. In experiments we show that these look-ahead screening rules outperform the active warm-start version of the Gap Safe rules.
Citation
@inproceedings{larsson2021,
author = {Larsson, Johan},
editor = {Makridis, Andreas and S. Milienos, Fotios and Papastamoulis,
Panagiotis and Parpoula, Christina and Rakitzis, Athanasios},
publisher = {Panteion University of Social and Political Sciences},
title = {Look-Ahead Screening Rules for the Lasso},
booktitle = {22nd European Young Statisticians Meeting - Proceedings},
pages = {61-65},
date = {2021-09-06},
address = {Athens, Greece},
url = {https://www.eysm2021.panteion.gr/files/Proceedings_EYSM_2021.pdf},
langid = {en-US},
abstract = {The lasso is a popular method to induce shrinkage and
sparsity in the solution vector (coefficients) of regression
problems, particularly when there are many predictors relative to
the number of observations. Solving the lasso in this
high-dimensional setting can, however, be computationally demanding.
Fortunately, this demand can be alleviated via the use of screening
rules that discard predictors prior to fitting the model, leading to
a reduced problem to be solved. In this paper, we present a new
screening strategy: look-ahead screening. Our method uses safe
screening rules to find a range of penalty values for which a given
predictor cannot enter the model, thereby screening predictors along
the remainder of the path. In experiments we show that these
look-ahead screening rules outperform the active warm-start version
of the Gap Safe rules.}
}