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

Clément Elvira (1) , Cédric Herzet (2)

1 IETR - Institut d'Électronique et des Technologies du numéRique
2 SIMSMART - SIMulation pARTiculaire de Modèles Stochastiques

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.

Keywords: SLOPE; safe screening; acceleration techniques; convex optimization

Domains: Machine Learning [cs.LG]

Clément Elvira, Cédric Herzet. Safe rules for the identification of zeros in the solution of the SLOPE problem. 2021. ⟨hal-03400322v1⟩