Safe rules for the identification of zeros in the solutions of the SLOPE problem
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In this paper we propose a methodology to accelerate the resolution of the so-called “Sorted L-One Penalized Estimation” (SLOPE) problem. Our method leverages the concept of “safe screening”, well-studied in the literature for group-separable sparsity-inducing norms, and aims at identifying the zeros in the solution of SLOPE. More specifically, we introduce a family of n! safe screening rules for this problem, where n is the dimension of the primal variable, and propose a tractable procedure to verify if one of these tests is passed. Our procedure has a complexity 𝒪(nlog n + LT) where T≤ n is a problem-dependent constant and L is the number of zeros identified by the tests. We assess the performance of our proposed method on a numerical benchmark and emphasize that it leads to significant computational savings in many setups.
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