**Brief course description: **The course will cover the main topics in high-dimensional probability

theory. High-dimensional probability is an area of probability theory that studies random objects

in Rn where the dimension n can be very large. The applications in data science of the introduced

theoretical tools will be discussed.

**Course topics:
**

Basic tail and concentration bounds: from Markov to Chernoff, sub-Gaussian vari-

ables and Hoeffding bounds, sub-exponential variables and Bernstein bounds, some one-

sided results, uniform laws of large numbers.

Sparse linear models in high dimensions: problem formulation and applications

and penalized estimators, recovery in the noiseless setting, estimation in noisy settings

and LASSO estimator, bounds on prediction error, variable or subset selection.

Nonparametric least squares: problem set-up, oracle inequalities, regularized esti-

mators.

Textbooks:

R. Vershynin (2018) High-dimensional probability. An introduction with applications in

Data Science. Cambridge University Press.

M. J. Wainwright (2019) High-dimensional statistics: A non-asymptotic viewpoint. Cam-

bridge University Press.