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 and Dr. Jianfei Li
Teaching Assistant: Adalbert Fono
Schedule and Venue
Lectures: Mon 10-12 in room B 041 and Thu 16-18 in room B 252
Exercises: Wed 14-16 in room 504 (Akademiestraße 7) and Wed 16-18 in room B 133. Please note that only one of the exercises is required as they cover the same content. You may choose the one that best fits your schedule.
Office Hour (Adalbert Fono): TBA
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=42378 (enrollment key is hdp)