Dr. Marwa Banna
High-dimensional Probability with Applications to Big Data Sciences
(Summer Semester 2019/20)Lecture Announcement
The lecture will be given in English.
News
- The final exam will take place on Wednesday, the 5th of August 2020
in Building E2 4, Room S6. Further details will be provided via email.
- The lecture will be given online using the platform Zoom. Therefore,
everybody who is interested in attending the lecture is asked to register
by writing an email to Marwa Banna before May 6, 2020. Further details
will be provided afterwards via email. As announced earlier, the first
lecture will be on Thursday, May 7, at 10:15am.
- Due to the ongoing spread of the coronavirus SARS-CoV-2, the start
of the main teaching period for the coming summer semester has been
postponed from 6 April to 4 May 2020. Accordingly, our first lecture
will take place on Thursday, May 7.
Lectures
- Thursday 10:00 -- 12:00, SR 10, building E2.4
Lectures Notes
Course description
With the fast growth of data sciences, there was a dramatic surge of interest and activity over the past two decades in high-dimensional probability that provides vital methods and tools for a wide range of applications. High-dimensional probability is the area of probability theory that studies random objects in R^n, where the dimension n can be very large. As classical probabilistic tools are no longer sufficient for most of the modern applications in data sciences, these lectures intend to cover partially this gap. The focus of the lectures is the non-asymptotic theory in high-dimensional probability with a view towards modern applications in big data sciences. Here is an incomplete list of topics that will be covered:- Basic concentration inequalities: Hoeffding, Bernstein, McDiarmid and Khintchine’s inequalities.
- Random vectors in high dimensions
- Matrix concentration inequalities
- Sub-Gaussian processes
- Dimension reduction with Johnson-Lindenstrauss lemma
- Community detection
- Covariance estimation and clustering
- Matrix completion
Excercises
Date : Tuesday 14:00 -- 16:00Place: online via the platform Zoom.
Assignments
Prerequisites
The lectures are self-contained and are open for students who have a good knowledge in linear algebra, measure theory and have succeeded Stochastics I. We will primarily rely on the following textbooks:- Roman Vershynin, High-dimensional probability: An introduction with applications
in data science, Cambridge University Press 2018.
- Martin J. Wainwright, High-dimensional statistics: A non-asymptotic viewpoint,
Cambridge University Press 2019.