New Convergence Rates for Function Approximation Using Kernel Methods

Young, David; Leith, Douglas

Permalink

https://hdl.handle.net/2142/130257 Copy

Description

Title

New Convergence Rates for Function Approximation Using Kernel Methods

Author(s)

• Young, David
• Leith, Douglas

Issue Date

2025-09-17

Keyword(s)

• Kernel methods
• Function approximation
• Reproducing kernel Hilbert space

Abstract

We derive new bounds for function approximation using reproducing kernel Hilbert spaces by analysing kernels which are k-times continuously differentiable, instead of kernels which are norm equivalent to Sobolev spaces. This means our method allows for a much wider choice of kernels, including the popular exponential quadratic and polynomial kernels, which are widely used in practical application of kernel methods. Our analysis also reveals other possible avenues for new and improved convergence bounds, depending on how we describe our target domain X and set of sample points X.

Publisher

Allerton Conference on Communication, Control, and Computing

Series/Report Name or Number

2025 61st Allerton Conference on Communication, Control, and Computing Proceedings

ISSN

2836-4503

Type of Resource

Text

Genre of Resource

Conference Paper/Presentation

Language

eng

Handle URL

https://hdl.handle.net/2142/130257

Copyright and License Information

Copyright 2025 is held by David Young and Douglas Leith.

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