Orthonormal Expansions for Translation-Invariant Kernels
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910427657535488 |
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| author | Tronarp, Filip Karvonen, Toni |
| author_facet | Tronarp, Filip Karvonen, Toni |
| contents | We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of $\mathscr{L}_2(\mathbb{R})$. This allows us to derive explicit expansions on the real line for (i) Matérn kernels of all half-integer orders in terms of associated Laguerre functions, (ii) the Cauchy kernel in terms of rational functions, and (iii) the Gaussian kernel in terms of Hermite functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2206_08648 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Orthonormal Expansions for Translation-Invariant Kernels Tronarp, Filip Karvonen, Toni Classical Analysis and ODEs Machine Learning Numerical Analysis We present a general Fourier analytic technique for constructing orthonormal basis expansions of translation-invariant kernels from orthonormal bases of $\mathscr{L}_2(\mathbb{R})$. This allows us to derive explicit expansions on the real line for (i) Matérn kernels of all half-integer orders in terms of associated Laguerre functions, (ii) the Cauchy kernel in terms of rational functions, and (iii) the Gaussian kernel in terms of Hermite functions. |
| title | Orthonormal Expansions for Translation-Invariant Kernels |
| topic | Classical Analysis and ODEs Machine Learning Numerical Analysis |
| url | https://arxiv.org/abs/2206.08648 |