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Mathematics of Machine Learning (Blockseminar)
Blockseminar 05.-19.09.2025
Inhalt:
In this hybrid course we aim to get acquainted with some of the recent progress in the mathematical understanding and theory of machine learning. Particular emphasis will be laid upon the implicit bias in supervised learning, as well as upon generative modelling.
The aim of the course is to get an overview of a series of recent articles and the methods developed therein.
The course is directed to non experts with a solid background in mathematics aiming to get an idea of recent progress in the mathematics of machine learning.
Active contribution in form of a presentation of a research paper (to be chosen) is required for each participant.
Link to seminar webpage (password on request via Alexandra Schulte): https://www.bgess.de/index.php/teaching/bielefeld-leipzig-online-seminar-ss25-mathematics-of-machine-learning/"
This event belongs to the joint special lecture + seminar on "Stochastic Optimization, and Reinforcement Learning and their Applications to Mathematical Finance".
The lecture “Introduction to Stochastic Optimization and Reinforcement Learning” serves as an introduction to analyzing common optimization problems appearing in modern machine learning applications. We will particularly focus on supervised learning and the dynamics of stochastic gradient descent, as well as Reinforcement Learning. This involves the analysis of stochastic processes in discrete time, whose behavior is closely linked to deterministic, as well as stochastic differential equations. While the general techniques for the asymptotic analysis of stochastic processes are introduced during the lecture, proper basic knowledge of probability theory (including martingale theory) is required.
The lecture will run in the first half of the semester, twice a week (Wednesday 14-16, MA144 and Thursday 8-10, MA 751).
In the second half of the semester, we will focus on applications to finance in the seminar "Applications of Stochastic Optimization and Reinforcement Learning to Mathematical Finance". In the seminar, each participant will present one research paper / chapter of a book. Possible topics for the seminar will be presented during the first lectures in the introductory part of this event.
