Irregular Sampling of High-Dimensional Functions in Reproducing Kernel Hilbert Spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909584169369600 |
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| author | Iske, Armin Ohlsen, Lennart |
| author_facet | Iske, Armin Ohlsen, Lennart |
| contents | We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas for tensor product kernels, where we show that determining irregular samples in lower dimensions can be composed to obtain a tensor of determining irregular samples in higher dimensions. This in turn reduces the computational complexity of sampling formulas for high-dimensional functions quite significantly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_13543 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Irregular Sampling of High-Dimensional Functions in Reproducing Kernel Hilbert Spaces Iske, Armin Ohlsen, Lennart Machine Learning Information Theory We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces, where we rely on irregular samples that are taken at determining sequences of data points. We place particular emphasis on sampling formulas for tensor product kernels, where we show that determining irregular samples in lower dimensions can be composed to obtain a tensor of determining irregular samples in higher dimensions. This in turn reduces the computational complexity of sampling formulas for high-dimensional functions quite significantly. |
| title | Irregular Sampling of High-Dimensional Functions in Reproducing Kernel Hilbert Spaces |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2504.13543 |