In this paper, we propose new methodologies todecrease the computational cost of safe screening tests forLASSO. We first introduce a new screening strategy, dubbedjoint screening test, which allows the rejection of a set of atomsby performing one single test. Our approach enables to findgood compromises between complexity of implementation andeffectiveness of screening. Second, we propose two new methodsto decrease the computational cost inherent to the constructionof the (so-called) safe region. Our numerical experiments showthat the proposed procedures lead to significant computationalgains as compared to standard methodologies.
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