  The sparse-group lasso performs both variable and group selection, making
simultaneous use of the strengths of the lasso and group lasso. It has found
widespread use in genetics, a field that regularly involves the analysis of
high-dimensional data, due to its sparse-group penalty, which allows it to
utilize grouping information. However, the sparse-group lasso can be
computationally more expensive than both the lasso and group lasso, due to the
added shrinkage complexity, and its additional hyper-parameter that needs
tuning. In this paper a novel dual feature reduction method, Dual Feature
Reduction (DFR), is presented that uses strong screening rules for the
sparse-group lasso and the adaptive sparse-group lasso to reduce their input
space before optimization. DFR applies two layers of screening and is based on
the dual norms of the sparse-group lasso and adaptive sparse-group lasso.
Through synthetic and real numerical studies, it is shown that the proposed
feature reduction approach is able to drastically reduce the computational cost
in many different scenarios.
