{"ID":2869893,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.14039","arxiv_id":"2509.14039","title":"On the Rate of Gaussian Approximation for Linear Regression Problems","abstract":"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.","short_abstract":"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...","url_abs":"https://arxiv.org/abs/2509.14039","url_pdf":"https://arxiv.org/pdf/2509.14039v1","authors":"[\"Marat Khusainov\",\"Marina Sheshukova\",\"Alain Durmus\",\"Sergey Samsonov\"]","published":"2025-09-17T14:42:13Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\",\"math.OC\"]","methods":"[]","has_code":false}