Look-Ahead Screening Rules for the Lasso

TL;DR

This paper introduces look-ahead screening rules for the lasso, which efficiently discard predictors during model fitting, significantly reducing computational effort in high-dimensional regression problems.

Contribution

The paper presents a novel look-ahead screening strategy that improves upon existing safe screening rules for the lasso, enabling more efficient predictor discarding along the regularization path.

Findings

Look-ahead screening outperforms Gap Safe rules in experiments.

Method reduces computational time for high-dimensional lasso problems.

Screening rules effectively identify predictors that will not enter the model.

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.