Reproducing kernel Hilbert spaces in the mean field limit

2023/02/28 by Christian Fiedler, Fiedler, Christian, Michaël Herty +7 · 1 citation
Computer Science · Environmental Science · Physics and Astronomy · #46E22 #74A25 #82B40 #82C40 #FOS: Computer and information sciences #FOS: Mathematics #Functional Analysis (math.FA) #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Soil Geostatistics and Mapping

paper · pdf · doi:10.48550/arxiv.2302.14446

openalex publication_date 2023/02/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Data-driven approximation of transfer operators for mean-field stochastic differential equations

Related

• On kernel-based statistical learning in the mean field limit
• Notes on Kernel Methods in Machine Learning
• Mean-field Analysis on Two-layer Neural Networks from a Kernel Perspective
• Reproducing Kernel Hilbert Space, Mercer's Theorem, Eigenfunctions, Nyström Method, and Use of Kernels in Machine Learning: Tutorial and Survey
• A Fourier-based inference method for learning interaction kernels in particle systems