Dimension-free bounds in high-dimensional linear regression via error-in-operator approach
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916624847601664 |
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| author | Noskov, Fedor Puchkin, Nikita Spokoiny, Vladimir |
| author_facet | Noskov, Fedor Puchkin, Nikita Spokoiny, Vladimir |
| contents | We consider a problem of high-dimensional linear regression with random design. We suggest a novel approach referred to as error-in-operator which does not estimate the design covariance $Σ$ directly but incorporates it into empirical risk minimization. We provide an expansion of the excess prediction risk and derive non-asymptotic dimension-free bounds on the leading term and the remainder. This helps us to show that auxiliary variables do not increase the effective dimension of the problem, provided that parameters of the procedure are tuned properly. We also discuss computational aspects of our method and illustrate its performance with numerical experiments. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_15437 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dimension-free bounds in high-dimensional linear regression via error-in-operator approach Noskov, Fedor Puchkin, Nikita Spokoiny, Vladimir Statistics Theory Machine Learning Methodology We consider a problem of high-dimensional linear regression with random design. We suggest a novel approach referred to as error-in-operator which does not estimate the design covariance $Σ$ directly but incorporates it into empirical risk minimization. We provide an expansion of the excess prediction risk and derive non-asymptotic dimension-free bounds on the leading term and the remainder. This helps us to show that auxiliary variables do not increase the effective dimension of the problem, provided that parameters of the procedure are tuned properly. We also discuss computational aspects of our method and illustrate its performance with numerical experiments. |
| title | Dimension-free bounds in high-dimensional linear regression via error-in-operator approach |
| topic | Statistics Theory Machine Learning Methodology |
| url | https://arxiv.org/abs/2502.15437 |