Web: http://arxiv.org/abs/2206.08648

June 20, 2022, 1:10 a.m. | Filip Tronarp, Toni Karvonen

cs.LG updates on arXiv.org arxiv.org

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) Mat\'ern 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.

arxiv math translation

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