Ensembles of Lasso Screening Rules

In order to solve large-scale lasso problems, screening algorithms have been developed that discard features with zero coefficients based on a computationally efficient screening rule. Most existing screening rules were developed from a spherical constraint and half-space constraints on a dual optimal solution. However, existing rules admit at most two half-space constraints due to the computational cost incurred by the half-spaces, even though additional constraints may be useful to discard more features. In this paper, we present AdaScreen, an adaptive lasso screening rule ensemble, which allows to combine any one sphere with multiple half-space constraints on a dual optimal solution. Thanks to geometrical considerations that lead to a simple closed form solution for AdaScreen, we can incorporate multiple half-space constraints at small computational cost. In our experiments, we show that AdaScreen with multiple half-space constraints simultaneously improves screening performance and speeds up lasso solvers.