On the Rate of Gaussian Approximation for Linear Regression Problems
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916954818740224 |
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| author | Khusainov, Marat Sheshukova, Marina Durmus, Alain Samsonov, Sergey |
| author_facet | Khusainov, Marat Sheshukova, Marina Durmus, Alain Samsonov, Sergey |
| contents | In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate upon the problem dimension $d$ and quantities related to the design matrix. When the number of iterations $n$ is known in advance, our results yield the rate of normal approximation of order $\sqrt{\log{n}/n}$, provided that the sample size $n$ is large enough. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_14039 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Rate of Gaussian Approximation for Linear Regression Problems Khusainov, Marat Sheshukova, Marina Durmus, Alain Samsonov, Sergey Machine Learning Optimization and Control 60F05, 62L20, 93E35 In this paper, we consider the problem of Gaussian approximation for the online linear regression task. We derive the corresponding rates for the setting of a constant learning rate and study the explicit dependence of the convergence rate upon the problem dimension $d$ and quantities related to the design matrix. When the number of iterations $n$ is known in advance, our results yield the rate of normal approximation of order $\sqrt{\log{n}/n}$, provided that the sample size $n$ is large enough. |
| title | On the Rate of Gaussian Approximation for Linear Regression Problems |
| topic | Machine Learning Optimization and Control 60F05, 62L20, 93E35 |
| url | https://arxiv.org/abs/2509.14039 |