Johannes Alt
Advanced Topics in Probability Theory
High-Dimensional Probability with applications to data science
Winter Term 2026/2027
Lecturer: Prof. Dr. Johannes Alt
This course provides an introduction to the tools required to understand probabilistic phenomena in high dimensions. Such phenomena are particularly relevant for applications to real life data where typically the number of measured quantities is comparable to the number of samples or even drastically exceeds it. Along the course, we will learn the probabilistic tools crucial for high-dimensional problems. They include concentration estimates and random matrix techniques. Moreover, we will see how these tools are applied to data science problems.
News
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List of topics
- Volumes in high dimensions
- Concentration inequalities
- Networks, random graphs and clustering
- To be continued
Prerequisites: Solid knowledge of measure, integration and probability theory including conditional expectation as well as linear algebra is necessary. Some knowledge in basic functional analysis (norms in finite dimensions, matrix norms, operator norm of a matrix) is helpful but can also be recalled in the lecture.
Literature
Books
- Afonso S. Bandeira, Amit Singer, Thomas Strohmer: Mathematics of Data Science, in preparation, preliminary version available at arXiv:2607.11938
- Roman Vershynin: High-dimensional probability, An Introduction with Applications in Data Science, Second Edition, 2026.
Lectures notes
- Afonso Bandeira, Ten Lectures and Forty-Two Open Problems in the Mathematics of Data Science, 2016