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Pattern recovery by SLOPE

Bogdan, Małgorzata LU ; Dupuis, Xavier ; Graczyk, Piotr ; Kołodziejek, Bartosz ; Skalski, Tomasz ; Tardivel, Patrick and Wilczyński, Maciej (2026) In Applied and Computational Harmonic Analysis 80.
Abstract

SLOPE is a popular method for dimensionality reduction in high-dimensional regression. Its estimated coefficients can be zero, yielding sparsity, or equal in absolute value, yielding clustering. As a result, SLOPE can eliminate irrelevant predictors and identify groups of predictors that have the same influence on the response. The concept of the SLOPE pattern allows us to formalize and study its sparsity and clustering properties. In particular, the SLOPE pattern of a coefficient vector captures the signs of its components (positive, negative, or zero), the clusters (groups of coefficients with the same absolute value), and the ranking of those clusters. This is the first paper to thoroughly investigate the consistency of the SLOPE... (More)

SLOPE is a popular method for dimensionality reduction in high-dimensional regression. Its estimated coefficients can be zero, yielding sparsity, or equal in absolute value, yielding clustering. As a result, SLOPE can eliminate irrelevant predictors and identify groups of predictors that have the same influence on the response. The concept of the SLOPE pattern allows us to formalize and study its sparsity and clustering properties. In particular, the SLOPE pattern of a coefficient vector captures the signs of its components (positive, negative, or zero), the clusters (groups of coefficients with the same absolute value), and the ranking of those clusters. This is the first paper to thoroughly investigate the consistency of the SLOPE pattern. We establish necessary and sufficient conditions for SLOPE pattern recovery, which in turn enable the derivation of an irrepresentability condition for SLOPE given a fixed design matrix X. These results lay the groundwork for a comprehensive asymptotic analysis of SLOPE pattern consistency.

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organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Irrepresentability condition, Linear regression, Pattern recovery, SLOPE
in
Applied and Computational Harmonic Analysis
volume
80
article number
101810
publisher
Elsevier
external identifiers
  • scopus:105015950633
ISSN
1063-5203
DOI
10.1016/j.acha.2025.101810
language
English
LU publication?
yes
id
e1138b23-0e0e-42d7-bdd6-f1f3d482cd1a
date added to LUP
2025-10-02 09:35:04
date last changed
2025-10-14 10:09:13
@article{e1138b23-0e0e-42d7-bdd6-f1f3d482cd1a,
  abstract     = {{<p>SLOPE is a popular method for dimensionality reduction in high-dimensional regression. Its estimated coefficients can be zero, yielding sparsity, or equal in absolute value, yielding clustering. As a result, SLOPE can eliminate irrelevant predictors and identify groups of predictors that have the same influence on the response. The concept of the SLOPE pattern allows us to formalize and study its sparsity and clustering properties. In particular, the SLOPE pattern of a coefficient vector captures the signs of its components (positive, negative, or zero), the clusters (groups of coefficients with the same absolute value), and the ranking of those clusters. This is the first paper to thoroughly investigate the consistency of the SLOPE pattern. We establish necessary and sufficient conditions for SLOPE pattern recovery, which in turn enable the derivation of an irrepresentability condition for SLOPE given a fixed design matrix X. These results lay the groundwork for a comprehensive asymptotic analysis of SLOPE pattern consistency.</p>}},
  author       = {{Bogdan, Małgorzata and Dupuis, Xavier and Graczyk, Piotr and Kołodziejek, Bartosz and Skalski, Tomasz and Tardivel, Patrick and Wilczyński, Maciej}},
  issn         = {{1063-5203}},
  keywords     = {{Irrepresentability condition; Linear regression; Pattern recovery; SLOPE}},
  language     = {{eng}},
  publisher    = {{Elsevier}},
  series       = {{Applied and Computational Harmonic Analysis}},
  title        = {{Pattern recovery by SLOPE}},
  url          = {{http://dx.doi.org/10.1016/j.acha.2025.101810}},
  doi          = {{10.1016/j.acha.2025.101810}},
  volume       = {{80}},
  year         = {{2026}},
}