On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces
Fuente:
arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908326028115968 |
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| author | Iske, Armin |
| author_facet | Iske, Armin |
| contents | We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the input data. We first prove error estimates in the kernel's RKHS norm. This leads us to new results concerning uniform convergence of kernel regression on compact domains. For Lipschitz continuous and Hölder continuous kernels, we prove convergence rates. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13623 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces Iske, Armin Machine Learning Numerical Analysis We analyse the convergence of sampling algorithms for functions in reproducing kernel Hilbert spaces (RKHS). To this end, we discuss approximation properties of kernel regression under minimalistic assumptions on both the kernel and the input data. We first prove error estimates in the kernel's RKHS norm. This leads us to new results concerning uniform convergence of kernel regression on compact domains. For Lipschitz continuous and Hölder continuous kernels, we prove convergence rates. |
| title | On the Convergence of Irregular Sampling in Reproducing Kernel Hilbert Spaces |
| topic | Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2504.13623 |