Reproducing kernel Hilbert spaces in the mean field limit

• URL: http://arxiv.org/abs/2302.14446v1
• Date: Tue, 28 Feb 2023 09:46:44 GMT
• Title: Reproducing kernel Hilbert spaces in the mean field limit
• Authors: Christian Fiedler, Michael Herty, Michael Rom, Chiara Segala, Sebastian Trimpe
• Abstract summary: kernels are function spaces generated by kernels, so called reproducing kernel Hilbert spaces. We show the rigorous mean field limit of kernels and provide a detailed analysis of the limiting reproducing Hilbert space.
• Score: 6.844996517347866
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Kernel methods, being supported by a well-developed theory and coming with efficient algorithms, are among the most popular and successful machine learning techniques. From a mathematical point of view, these methods rest on the concept of kernels and function spaces generated by kernels, so called reproducing kernel Hilbert spaces. Motivated by recent developments of learning approaches in the context of interacting particle systems, we investigate kernel methods acting on data with many measurement variables. We show the rigorous mean field limit of kernels and provide a detailed analysis of the limiting reproducing kernel Hilbert space. Furthermore, several examples of kernels, that allow a rigorous mean field limit, are presented.

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