Michael Hartz

Seminar on reproducing kernels and machine learning

(Summer term 2021)


Time and Place

The seminar will be held via MS Teams. The meeting time will be determined at the organizational meeting. The seminar will be held in either English or German, depending on the audience.


Reproducing kernels are a concept in mathematical analysis that can be traced back at least 100 years. They were introduced to understand problems in harmonic analysis and complex analysis and have since become a vibrant subject in pure mathematics.

Remarkably, in the 1990s, reproducing kernels emerged in computer science in the context of machine learning. At that time, a new type of learning algorithm, the support vector machine, was developed. In this setting, reproducing kernels give rise to theoretically elegant machines that can efficiently perform non-linear classification.

The goal of this seminar is to understand the basic theory of reproducing kernels and how it can be used to develop machine learning algorithms.


Prerequisites are undergraduate calculus and linear algebra as well as basic knowledge of probability theory. Thus, the seminar is suitable for students in mathematics having completed Analysis 1-2, Linear Algebra 1-2 and possessing familiarity with basic probability theory. Moreover, the seminar is suitable for computer science students who have completed Mathematik für Informatiker 1-3.


See also the library site

Main textbook:
Schölkopf, Bernhard and Smola, Alexander J., Learning with Kernels , 2002.

Additional literature:
Berg, Christian, Christensen, Jens Peter Reus and Ressel, Paul, Harmonic analysis on semigroups : theory of positive definite and related functions , 1984
Davidson, Kenneth R. and Donsig, Allan P., Real Analysis and Applications: Theory in Practice , 2010
Paulsen, Vern I. and Raghupathi, Mrinal, An introduction to the theory of reproducing kernel Hilbert spaces , 2016.
Steinwart, Ingo and Christmann, Andreas, Support Vector Machines , 2008.

Last update: March 18, 2021   Michael Hartz