Bavarian AI Chair for Mathematical Foundations of Artificial Intelligence

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High-Dimensional Probability

Course Description

Probabilistic methods are a fundamental tool for data science and machine learning. Apart from allowing a deeper understanding of the geometry of high-dimensional spaces (in which data normally lives), they open up resource efficient ways to solve deterministic problems.

This lecture will provide a fundamental probabilistic toolbox for analyzing problems in high dimensions. The topics we discuss will encompass:

  • Concentration inequalities
  • Covering arguments
  • Decoupling
  • Symmetrization
  • Chaining techniques

The course is targeted at Master students from mathematics. Basic knowledge of probability theory is highly recommended.

Lecturer: Prof. Johannes Maly

Teaching Assistant: Stefan Kolek

Schedule and Venue

Lectures (Prof. Johannes Maly): Tue 10-12 and Thu 10-12 in room B 252

Exercises (Stefan Kolek): Mo 14-16 and Mo 16-18 in room B 251. Please note that only one of the exercises, either Monday 14-16 or Monday 16-18, is mandatory as they cover the same content. You may choose the one that best fits your schedule.

Office Hour (Stefan Kolek): Mo 11-12 in Akademiestr. 7, floor 5, room 511. Please email me the day before office hours to let me know if you plan to attend.

Creditable Modules

Master in Mathematics: WP35 Fortgeschrittene Themen aus der künstlichen Intelligenz und Data Science (9 ECTS)
Master in Mathematics: WP27 Fortgeschrittene Themen aus der Stochastik (9 ECTS)
Master in Financial and Insurance Mathematics: WP13 Advanced Topics in Mathematics A (9 ECTS)


Register at moodle (enrollment key is hdp).