  The lasso model has been widely used for model selection in data mining,
machine learning, and high-dimensional statistical analysis. However, with the
ultrahigh-dimensional, large-scale data sets now collected in many real-world
applications, it is important to develop algorithms to solve the lasso that
efficiently scale up to problems of this size. Discarding features from certain
steps of the algorithm is a powerful technique for increasing efficiency and
addressing the Big Data challenge. In this paper, we propose a family of hybrid
safe-strong rules (HSSR) which incorporate safe screening rules into the
sequential strong rule (SSR) to remove unnecessary computational burden. In
particular, we present two instances of HSSR, namely SSR-Dome and SSR-BEDPP,
for the standard lasso problem. We further extend SSR-BEDPP to the elastic net
and group lasso problems to demonstrate the generalizability of the hybrid
screening idea. Extensive numerical experiments with synthetic and real data
sets are conducted for both the standard lasso and the group lasso problems.
Results show that our proposed hybrid rules can substantially outperform
existing state-of-the-art rules.
