Gather and Conquer: Region-Based Strategies to Accelerate Safe Screening Tests

In this paper, we propose new methodologies to decrease the computational cost of safe screening tests for LASSO. We first introduce a new screening strategy, dubbed "joint screening test," which allows the rejection of a set of atoms by performing one single test. Our approach enables to find good compromises between complexity of implementation and effectiveness of screening. Second, we propose two new methods to decrease the computational cost inherent to the construction of the (so-called) "saferegion." Our numerical experiments show that the proposed procedures lead to significant computational gains as compared to standard methodologies.