Look-Ahead Screening Rules for the Lasso

Lasso
Screening Rules
Authors

Johan Larsson

Published

29 June 2021

Details

22nd European Young Statisticians Meeting - Proceedings, Athens, Greece

Links
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.

 

Citation

BibTeX 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.}
}
For attribution, please cite this work as:
Larsson, Johan. 2021. ā€œLook-Ahead Screening Rules for the Lasso.ā€ In 22nd European Young Statisticians Meeting - Proceedings, edited by Andreas Makridis, Fotios S. Milienos, Panagiotis Papastamoulis, Christina Parpoula, and Athanasios Rakitzis, 61ā€“65. Athens, Greece: Panteion University of Social and Political Sciences. https://www.eysm2021.panteion.gr/files/Proceedings_EYSM_2021.pdf.