{"ID":2881826,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.11274","arxiv_id":"2508.11274","title":"Uniform convergence for Gaussian kernel ridge regression","abstract":"This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical understanding of KRR with the Gaussian kernel, where no such rates were previously known. In addition, we prove a polynomial $L^{2}$-convergence rate in the case, where the Gaussian kernel's width parameter is fixed. This also contributes to the broader understanding of smooth kernels, for which previously only sub-polynomial $L^{2}$-rates were known in similar settings. Together, these results provide new theoretical justification for the use of Gaussian KRR with fixed hyperparameters in nonparametric regression.","short_abstract":"This paper establishes the first polynomial convergence rates for Gaussian kernel ridge regression (KRR) with a fixed hyperparameter in both the uniform and the $L^{2}$-norm. The uniform convergence result closes a gap in the theoretical understanding of KRR with the Gaussian kernel, where no such rates were previously...","url_abs":"https://arxiv.org/abs/2508.11274","url_pdf":"https://arxiv.org/pdf/2508.11274v2","authors":"[\"Paul Dommel\",\"Rajmadan Lakshmanan\"]","published":"2025-08-15T07:20:31Z","proceeding":"stat.ML","tasks":"[\"stat.ML\",\"cs.LG\"]","methods":"[]","has_code":false}