Deep and greedy kernel methods: Algorithms, analysis and applications

Speaker: Dr. Tizian Wenzel, University of Hamburg

Abstract: Kernel methods are a versatile class of tools widely used in machine learning, numerical approximation, and scientific computing. In this talk, we discuss recent advancements in deep and greedy kernel methods, highlighting several applications. In the context of (greedy) kernel interpolation, we introduce the framework of \beta-greedy algorithms and provide a detailed convergence analysis. Additional results include discussions on the optimal distribution of interpolation points, stability and optimality of convergence rates, and inverse theorems. For deep kernel methods, we focus on two-layered kernels, which can be interpreted as data-adapted anisotropic kernels. We discuss the optimization and analysis of these kernels, supported by numerical experiments that demonstrate their effectiveness in numerical approximation and machine learning tasks.

Biography: Dr. Wenzel completed his Bachelor in Physics (2013–2016) and his Master in Mathematics (2016–2019) at the University of Stuttgart. From 2019 to October 2023, he pursued a PhD at the SimTech Cluster of Excellence under Prof. Bernard Haasdonk, with research stays at KU Leuven (Prof. Johan Suykens) and the University of Genova (Prof. Lorenzo Rosasco). Currently, he is a Postdoctoral fellow at the University of Hamburg (Nov 2023–Oct 2024) under Prof. Armin Iske. From mid-October 2024, he will join LMU Munich as Akademischer Rat working with Prof. Holger Rauhut.

Host: Prof. Michael Multerer