Welcome to my course in high dimensional probability. I am Roman Vershynin, professor of mathematics at the University of California, Irvine, and the author of the textbook "High dimensional probability. An introduction with applications in Data Science."
This course builds probabilistic foundations for theoretical research in modern data science. You will learn some methods that form an essential toolbox for anyone looking to do mathematical work in machine learning, theoretical computer science, theoretical statistics, signal processing, etc.
The course is suitable for students in mathematics, statistics, computer science, and electrical engineering. A solid background in undergraduate linear algebra, real analysis, and probability theory are minimum prerequisites. Some familiarity with metric, Hilbert and normed spaces is a plus, but is not required. Knowledge of measure theory is not required.The course consists of 41 video lectures and 13 homework sets. It was taught remotely at Kyiv National University in Fall of 2022 and 2023, during the Russian invasion of Ukraine. The unparalleled determination of Ukrainian students to study mathematics despite the hardships of the war was a tremendous source of inspiration for me.
Some parts of this course are loosely based on my book, the draft of which you can download for free.