1. Sampling-based Nyström Approximation and Kernel Quadrature
- Author
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Hayakawa, Satoshi, Oberhauser, Harald, and Lyons, Terry
- Subjects
FOS: Computer and information sciences ,FOS: Mathematics ,Machine Learning (stat.ML) ,Numerical Analysis (math.NA) ,Machine Learning (cs.LG) - Abstract
We analyze the Nyström approximation of a positive definite kernel associated with a probability measure. We first prove an improved error bound for the conventional Nyström 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 Nyström 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., 22 pages, ICML 2023 camera-ready version. Typos fixed
- Published
- 2023
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