2nd degree (Master)
Coordinator Office Hours:
Prof Zemer Kosloff
The course will serve as an introduction to the methods of analyzing high dimensional statistical models. The first part will deal with the basic of tail and concentration bounds, sub-Gaussian random variables, entropic methods and uniform laws of large numbers.
After that we aim to apply these methods to some problems such as covariance estimators, sparse-linear regression and the Lasso algorithm.
Learning outcomes - On successful completion of this module, students should be able to:
Be familiar with the mathematical foundations and methods underlying modern research in the rapidly evolving field of high-dimensional statistics.
Teaching arrangement and method of instruction:
0) Introduction and some nice examples.
1) Basic tail bounds (Chernoff, Hoeffelding inequalities and martingale difference methods).
2) SubGaussian random variables, equivalent definitions and the sub-Gaussian norm.
3) Uniform laws of large numbers, Rademacher complexity and Vapnik-Chernovakis dimension.
4) Metric entropy and its uses: Covering, Packing, chainning and Dudley's integral.
5) Random matrices and covariance estimation.
6) Sparse linear regression.
Additional Reading Material:
a) M.J. Wainwright. High-Dimensional Statistics, A Non-Asymptotic Viewpoint. Cambridge university press.
b) R. Vershynin, Introduction to the non-asymptotic analysis of random matrices. Cambridge University Press,
c) A New Look at Independence – Special Invited Paper, by M. Talagrand, the Annals of Applied
Probability, 24(1),1–34, 1996.
End of year written/oral examination 0 %
Presentation 50 %
Participation in Tutorials 0 %
Project work 0 %
Assignments 50 %
Reports 0 %
Research project 0 %
Quizzes 0 %
Other 0 %
The interested students must have completed the course "introduction to probability theory and statistics. Knowledge in measure theory and continuous probability is an advantage.