Strong Screening Rules for Group-based SLOPE Models

TL;DR

This paper introduces strong screening rules for group-based SLOPE models, significantly reducing computational costs and enabling high-dimensional data analysis, especially in genetics.

Contribution

Develops strong screening rules for group SLOPE and sparse-group SLOPE, applicable to a broader family of group-based OWL models, enhancing computational efficiency.

Findings

Screening rules significantly accelerate model fitting.

Rules enable application to high-dimensional genetic data.

Applicable to a wider family of OWL models.

Abstract

Tuning the regularization parameter in penalized regression models is an expensive task, requiring multiple models to be fit along a path of parameters. Strong screening rules drastically reduce computational costs by lowering the dimensionality of the input prior to fitting. We develop strong screening rules for group-based Sorted L-One Penalized Estimation (SLOPE) models: Group SLOPE and Sparse-group SLOPE. The developed rules are applicable to the wider family of group-based OWL models, including OSCAR. Our experiments on both synthetic and real data show that the screening rules significantly accelerate the fitting process. The screening rules make it accessible for group SLOPE and sparse-group SLOPE to be applied to high-dimensional datasets, particularly those encountered in genetics.