We provide a necessary and sufficient condition for the uniqueness of penalized least-
squares estimators whose penalty term is given by a norm with a polytope unit ball, covering …

The SLOPE estimator has the particularity of having null components (sparsity) and
components that are equal in absolute value (clustering). The number of clusters depends …

SLOPE is a popular method for dimensionality reduction in the high-dimensional regression.
Indeed some regression coefficient estimates of SLOPE can be null (sparsity) or can be …

We consider the framework of penalized estimation where the penalty term is given by a real-
valued polyhedral gauge, which encompasses methods such as LASSO (and many variants …

Résumé L'estimateur SLOPE (acronyme signifiant≪ Sorted L One Penalized Estimation≫)
est défini comme une solution d'un probleme d'optimisation convexe ou le terme de pénalité …

We concern new applications of discrete geometry and combinatorics in modern statistics.
First of them focuses on the use of penalized linear regresion methods. We start our …

Subdifferential formula for the sorted 1 norm attracted lot of attention recently to derive
screening procedures for SLOPE [5, 7], clustering and sparsity properties for SLOPE [1, 10] …

L'estimateur SLOPE a la particularité d'avoir des composantes nulles (parcimonie) et des
composantes égales en valeur absolue (appariement). Le nombre de groupes …

Abstract The Octagonal Shrinkage and Clustering Algorithm for Regression (OSCAR) and
the related Ordered Weighted i1 (OWL) penalized estimator have the particularity to exhibit …

The SLOPE estimator has the particularity of having null components (sparsity) and
components that are equal in absolute value (clustering). The number of clusters depends …