Strong Screening Rules for Group-based SLOPE Models
This work addresses a computational bottleneck for researchers and practitioners using group-based SLOPE models, particularly in genetics, but it is incremental as it extends existing screening rules to new model variants.
The paper tackles the computational cost of tuning regularization parameters in penalized regression by developing strong screening rules for group-based SLOPE models, which significantly accelerate the fitting process and enable application to high-dimensional datasets like genetics.
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.