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arXiv · 2301.09517

Sampling-based Nystr\"om Approximation and Kernel Quadrature

Satoshi Hayakawa·Harald Oberhauser·Terry Lyons
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Abstract

We analyze the Nystr\"om approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nystr\"om approximation with i.i.d. sampling and singular-value decomposition in the continuous regime; the proof techniques are borrowed from statistical learning theory. We further introduce a refined selection of subspaces in Nystr\"om approximation with theoretical guarantees that is applicable to non-i.i.d. landmark points. Finally, we discuss their application to convex kernel quadrature and give novel theoretical guarantees as well as numerical observations.

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Satoshi Hayakawa, Harald Oberhauser, Terry Lyons. 2023-01-23. Sampling-based Nystr\"om Approximation and Kernel Quadrature. https://arxiv.org/abs/2301.09517

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