Safe Screening Rules for Group SLOPE

TL;DR

This paper introduces a safe screening rule for Group SLOPE that efficiently identifies inactive groups, significantly reducing computational costs and memory usage in high-dimensional sparse learning with group structures.

Contribution

The paper proposes a novel safe screening rule for Group SLOPE that handles block non-separable effects, improving efficiency while maintaining accuracy.

Findings

Effective detection of inactive feature groups

Significant improvements in computational efficiency

Seamless integration with existing solvers

Abstract

Variable selection is a challenging problem in high-dimensional sparse learning, especially when group structures exist. Group SLOPE performs well for the adaptive selection of groups of predictors. However, the block non-separable group effects in Group SLOPE make existing methods either invalid or inefficient. Consequently, Group SLOPE tends to incur significant computational costs and memory usage in practical high-dimensional scenarios. To overcome this issue, we introduce a safe screening rule tailored for the Group SLOPE model, which efficiently identifies inactive groups with zero coefficients by addressing the block non-separable group effects. By excluding these inactive groups during training, we achieve considerable gains in computational efficiency and memory usage. Importantly, the proposed screening rule can be seamlessly integrated into existing solvers for both batch and stochastic algorithms. Theoretically, we establish that our screening rule can be safely employed with existing optimization algorithms, ensuring the same results as the original approaches. Experimental results confirm that our method effectively detects inactive feature groups and significantly boosts computational efficiency without compromising accuracy.