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 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)