Universität Wien

250085 SE Seminar Analysis (2023S)

4.00 ECTS (2.00 SWS), SPL 25 - Mathematik
Continuous assessment of course work
Moodle

Registration/Deregistration

Note: The time of your registration within the registration period has no effect on the allocation of places (no first come, first served).

Details

max. 25 participants
Language: English

Lecturers

Classes (iCal) - next class is marked with N

  • Tuesday 07.03. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 14.03. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 21.03. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 28.03. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 18.04. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 25.04. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 02.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 09.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 16.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 23.05. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 06.06. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 13.06. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 20.06. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock
  • Tuesday 27.06. 15:00 - 16:30 Seminarraum 9 Oskar-Morgenstern-Platz 1 2.Stock

Information

Aims, contents and method of the course

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.

Assessment and permitted materials

A 90-minute presentation and active participation. Depending on the number of participants, more than one presentation may be possible.

Minimum requirements and assessment criteria

A 90-minute presentation and active participation. Depending on the number of participants, more than one presentation may be possible. The teacher will assess the participants' presentations and work.

Examination topics

See "contents" above.

Reading list

Main bibliography:

- 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

Additional bibliography:

- High-Dimensional Statistics, A Non-Asymptotic Viewpoint. Martin J. Wainwright, Cambridge University Press, 2019.

Association in the course directory

MANS

Last modified: Tu 14.03.2023 12:09