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Journal Articles SIAM Journal on Mathematics of Data Science Year : 2023

Safe rules for the identification of zeros in the solution of the SLOPE problem

Abstract

In this paper we propose a methodology to accelerate the resolution of the socalled "Sorted LOne 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(n log 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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hal-03400322 , version 1 (25-10-2021)
hal-03400322 , version 2 (15-04-2022)

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Clément Elvira, Cédric Herzet. Safe rules for the identification of zeros in the solution of the SLOPE problem. SIAM Journal on Mathematics of Data Science, 2023, 5 (1), pp.147-173. ⟨10.1137/21M1457631⟩. ⟨hal-03400322v2⟩
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