2021/10/22 by Clément Elvira, Elvira, Clément, Cédric Herzet +1 · 2 citations
Biochemistry, Genetics and Molecular Biology · Mathematics · #Advanced Statistical Methods and Models #Cancer, Lipids, and Metabolism #FOS: Computer and information sciences #Machine Learning (cs.LG) #Statistical Methods and Inference
paper · doi:10.48550/arxiv.2110.11784
openalex publication_date 2021/10/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 derive a set of \(\tfracn(n+1)2\) inequalities for each element of the \(n\)-dimensional primal vector and prove that the latter can be safely screened if some subsets of these inequalities are verified. We propose moreover an efficient algorithm to jointly apply the proposed procedure to all the primal variables. 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. Numerical experiments confirm that, for a prescribed computational budget, the proposed methodology leads to significant improvements of the solving precision.