Information Geometry in Machine Learning

SoSe 2026

Course Description

Information geometry (IG) is an interdisciplinary field that applies techniques from differential geometry to the study of probability theory and statistics. It focuses on statistical manifolds, which are Riemannian manifolds whose points correspond to probability distributions. In this course, we give a general introduction to the field with the aim of using IG to formulate and analyze machine learning (ML) problems.

Course Outline

The course starts with a general introduction to machine learning and to several complementary approaches for the theoretical study of learning problems, and develops how IG complements existing directions. From there, we formally study the geometry of statistical models by introducing central concepts of IG. Generalizing these ideas to arbitrary manifolds, we build the foundation for studying more general machine learning models. Finally, we apply these concepts to analyze fundamental machine learning ideas such as natural gradient descent, and discuss state-of-the-art research advances of IG in ML.

The course consists of two lecture hours and two tutorial hours per week. The lectures introduce the main results and concepts of IG, including proofs. In the tutorials, we apply these results to explicit sample problems and illustrate them through numerical simulations.

Prerequisites

The course is targeted at Master’s students in mathematics. Basic knowledge of machine learning, differential geometry, probability, statistics, and Python programming is recommended but not required. We will introduce all necessary concepts for following the course throughout the semester (the first tutorial will include a short introduction to Python programming).

Schedule and Venue

  • Lecture (by Dr. Pascal Esser) Tuesday 12:00 - 14:00, Room B 046
  • Tutorial (by Dr. Pascal Esser) Wednesday 12:00 - 14:00, Room B 046

Creditable Modules

A total of 6 ECTS points can be earned for this course. It can be graded as part of the following modules:

  • Master of Science in Mathematik: Modul WP42 “ ¨Uberblick ¨uber ein aktuelles Forschungsgebiet B”
  • Master of Science in Finanz- und Versicherungsmathematik: Modul WP23 “Advanced Topics in Computer and Data Science B”

Registration

TBA