Irregular Sampling of High-Dimensional Functions in Reproducing Kernel Hilbert Spaces

Published: 25 Mar 2025, Last Modified: 20 May 2025SampTA 2025 OralEveryoneRevisionsBibTeXCC BY 4.0
Session: General
Keywords: Sampling formulas, irregular sampling, reproducing kernel Hilbert spaces
TL;DR: We develop sampling formulas for high-dimensional functions in reproducing kernel Hilbert spaces
Abstract:

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.

Submission Number: 27
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