250085 SE Seminar Analysis (2023S)

The seminar will provide an introduction to high-dimensional probability and applications

* Contents:

We will mainly follow the book:

High-Dimensional Probability, An Introduction with Applications in Data Science. Roman Vershynin, Cambridge University Press, 2018

https://www.math.uci.edu/~rvershyn/papers/HDP-book/HDP-book.pdf

The course is intended for masters and doctoral students and provides an introduction to methods that lie at the foundation of modern research in data sciences.

Some core topics are:

1) Concentration of sums of independent random variables

2) Random vectors in high dimensions

3) Random matrices

4) Applications in data science (e.g., principal component analysis in high dimension, tightness of convex relaxations and semidefinite programming, maximum cut for graphs, detection of communities in networks, recovery of sparse vectors from few measurements.)

The course will be adapted to the participants' interests and background.

* Format:

Each meeting will be in charge of a seminar participant. We will work out the material in detail and provide complete proofs.

* Prerequisites:

Basic probability and linear algebra. Familiarity with measure theory is not essential but helpful.