  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 for 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.
