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)
Registration
Register at moodle https://moodle.lmu.de/course/view.php?id=30094 (enrollment key is hdp).