The Hebrew University Logo
Syllabus High dimensional statistics - 80629
close window close
PDF version
Last update 02-09-2021
HU Credits: 3

Degree/Cycle: 2nd degree (Master)

Responsible Department: Mathematics

Semester: 1st Semester

Teaching Languages: Hebrew

Campus: E. Safra

Course/Module Coordinator: Zemer Kosloff

Coordinator Email:

Coordinator Office Hours:

Teaching Staff:
Prof Zemer Kosloff

Course/Module description:
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.

Course/Module aims:

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.

Attendance requirements(%):

Teaching arrangement and method of instruction: Lectures

Course/Module Content:
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.

Required Reading:

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.

Course/Module evaluation:
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 %

Additional information:
The interested students must have completed the course "introduction to probability theory and statistics. Knowledge in measure theory and continuous probability is an advantage.
Students needing academic accommodations based on a disability should contact the Center for Diagnosis and Support of Students with Learning Disabilities, or the Office for Students with Disabilities, as early as possible, to discuss and coordinate accommodations, based on relevant documentation.
For further information, please visit the site of the Dean of Students Office.