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Pattern recovery and signal denoising by SLOPE when the design matrix is orthogonal

Bartosz Kolodziejek
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Maciej Wilczyński
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Abstract

Sorted ℓ1 Penalized Estimator (SLOPE) is a relatively new convex regularization method for fitting high-dimensional regression models. SLOPE allows to reduce the model dimension by nullifying some of the regression coefficients and by equalizing some of nonzero coefficients. This allows to identify situations where some of true regression coefficients are equal. In this article we will introduce the SLOPE pattern, i.e., the set of relations between the true regression coefficients, which can be identified by SLOPE. We will also present new results on the strong consistency of SLOPE estimators and on the strong consistency of pattern recovery by SLOPE when the design matrix is orthogonal and illustrate advantages of the SLOPE clustering in the context of high frequency signal denoising. * The authors want to thank Ma lgorzata Bogdan, Patrick Tardivel, Wojciech Rejchel and TomaszŻak for references, comments and discussion.
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Dates and versions

hal-03610548 , version 1 (16-03-2022)

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  • HAL Id : hal-03610548 , version 1

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Tomasz Skalski, Piotr Graczyk, Bartosz Kolodziejek, Maciej Wilczyński. Pattern recovery and signal denoising by SLOPE when the design matrix is orthogonal. 2022. ⟨hal-03610548⟩
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