Pattern recovery by SLOPE
Abstract
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 equal in absolute value (clustering). Consequently, SLOPE may eliminate irrelevant predictors and may identify groups of predictors having the same influence on the vector of responses. The notion of SLOPE pattern allows to derive theoretical properties on sparsity and clustering by SLOPE. Specifically, the SLOPE pattern of a vector provides: the sign of its components (positive, negative or null), the clusters (indices of components equal in absolute value) and clusters ranking. In this article we give a necessary and sufficient condition for SLOPE pattern recovery of an unknown vector of regression coefficients.
Keywords
Cite
@article{arxiv.2203.12086,
title = {Pattern recovery by SLOPE},
author = {Małgorzata Bogdan and Xavier Dupuis and Piotr Graczyk and Bartosz Kołodziejek and Tomasz Skalski and Patrick Tardivel and Maciej Wilczyński},
journal= {arXiv preprint arXiv:2203.12086},
year = {2025}
}
Comments
55 pages, 8 figures. The order of authors is alphabetical