Safe Screening With Variational Inequalities and Its Application to LASSO

TL;DR

This paper introduces Sasvi, a novel safe screening method for LASSO that leverages variational inequalities to efficiently identify zero coefficients, significantly reducing computational costs in high-dimensional sparse learning.

Contribution

Sasvi is a new safe screening approach using variational inequalities, providing stronger rules and monotonic properties for LASSO feature elimination.

Findings

Sasvi outperforms existing screening methods in efficiency.

Sasvi can identify a regularization parameter for feature removal.

Experimental results confirm Sasvi's effectiveness on synthetic and real data.

Abstract

Sparse learning techniques have been routinely used for feature selection as the resulting model usually has a small number of non-zero entries. Safe screening, which eliminates the features that are guaranteed to have zero coefficients for a certain value of the regularization parameter, is a technique for improving the computational efficiency. Safe screening is gaining increasing attention since 1) solving sparse learning formulations usually has a high computational cost especially when the number of features is large and 2) one needs to try several regularization parameters to select a suitable model. In this paper, we propose an approach called "Sasvi" (Safe screening with variational inequalities). Sasvi makes use of the variational inequality that provides the sufficient and necessary optimality condition for the dual problem. Several existing approaches for Lasso screening can be casted as relaxed versions of the proposed Sasvi, thus Sasvi provides a stronger safe screening rule. We further study the monotone properties of Sasvi for Lasso, based on which a sure removal regularization parameter can be identified for each feature. Experimental results on both synthetic and real data sets are reported to demonstrate the effectiveness of the proposed Sasvi for Lasso screening.