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| Auteurs principaux: | , , , , , , |
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| Format: | Preprint |
| Publié: |
2022
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2203.12086 |
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| _version_ | 1866916953519554560 |
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| author | Bogdan, Małgorzata Dupuis, Xavier Graczyk, Piotr Kołodziejek, Bartosz Skalski, Tomasz Tardivel, Patrick Wilczyński, Maciej |
| author_facet | Bogdan, Małgorzata Dupuis, Xavier Graczyk, Piotr Kołodziejek, Bartosz Skalski, Tomasz Tardivel, Patrick Wilczyński, Maciej |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2203_12086 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Pattern recovery by SLOPE Bogdan, Małgorzata Dupuis, Xavier Graczyk, Piotr Kołodziejek, Bartosz Skalski, Tomasz Tardivel, Patrick Wilczyński, Maciej Statistics Theory 62J05 (Primary) 62J07 (Secondary) 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. |
| title | Pattern recovery by SLOPE |
| topic | Statistics Theory 62J05 (Primary) 62J07 (Secondary) |
| url | https://arxiv.org/abs/2203.12086 |