Reproducing Kernels in and for the Mean Field Limit

Title

Reproducing Kernels in and for the Mean Field Limit

Speaker

Christian Fiedler - RWTH Aachen University

Abstract

Large-scale multiagent systems play an important role in many areas of engineering, mathematics, and natural sciences. One way to handle systems with a very large number of agents is the mean field limit from kinetic theory. In this talk, we present recent work on the connection between this limit and kernel methods and their underlying theory. Motivated by certain learning problems for large-scale interacting particle systems, we investigate the mean field limit of kernels and their reproducing kernel Hilbert spaces. In turn, this is applied to kernel-based statistical learning. We establish appropriate mean field limit notions of statistical learning problems, and prove mean field convergence of support vector machines for these problems. On the one hand, this provides a solid theoretical foundation for learning problems on large-scale interacting particle systems, and on the other hand, it forms a new kind of large-scale limit in the theory of machine learning. Prompted by this fruitful interaction of mean field limits and kernels, we also consider the use of kernel methods and their theory in the context of kinetic theory. In particular, we report on recent work concerning mean field limits of discrete-time multiagent systems, where the theory of reproducing kernel is used to prove existence of this limit, demonstrating that reproducing kernels can also play a role for kinetic theory.

Bio

Christian Fiedler is a final year PhD student and scientific assistant at the Institute for Data Science in Mechanical Engineering (DSME) at RWTH Aachen University. He holds a B.Sc. degree in Mathematics from the University of Bayreuth, a M.Phil. degree in Computational Biology from the University of Cambridge, and a M.Sc. degree in Mathematics from the Technical University of Munich. During his studies, he was supported by the Max Weber scholarship program. In 2019, he joined the Max Planck Institute for Intelligent Systems and the University of Stuttgart as a PhD student, before transferring to RWTH Aachen University in 2021. He has broad research interests in machine learning and control theory, and the intersection thereof, with a particular focus on kernel methods.

When

Monday, February 24th at 16:00

Where

Room 322, UniGe DIBRIS/DIMA, Via Dodecaneso 35