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Vorlesung + Übung: Hochdimensionale Wahrscheinlichkeitstheorie mit Anwendungen in Data Science - Details
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General information

Course name Vorlesung + Übung: Hochdimensionale Wahrscheinlichkeitstheorie mit Anwendungen in Data Science
Course number MTH-2750
Semester SS 2024
Current number of participants 18
Home institute Stochastik und ihre Anwendungen
Courses type Vorlesung + Übung in category Teaching
Next date Tuesday, 16.04.2024 08:15 - 09:45, Room: (1009/L)
Participants The course is open to Master students of Mathematics, Wi-Mathe, MRM, Data Science. Perfectly suited for Math + Computer Science track, also interested PhD students are welcome to attend.
Pre-requisites Probability + Linear Algebra.
Learning organisation Two lectures per week plus exercise session
Online/Digitale Veranstaltung Veranstaltung wird in Präsenz abgehalten.
Hauptunterrichtssprache englisch
Literaturhinweise Vershynin R. High-Dimensional Probability: An Introduction with Applications in Data Science. Cambridge University Press; 2018.

Rooms and times

(1009/L)
Tuesday: 08:15 - 09:45, weekly (13x)
(1005 / L)
Thursday: 08:15 - 09:45, weekly (11x)
(1010/L)
Thursday: 15:45 - 17:15, weekly (12x)

Fields of study

Module assignments

Comment/Description

We discuss a number of special topics in probability theory related to random vectors, random matrices and random projections. We cover basic theoretical tools to analyse these objects and present applications of high-dimensional probability in data science. In more details, we cover the following topics:

1. Concentration inequalities (Hoeffding's, Bernstein's inequalities etc)
2. Random matrices (Covering and packing arguments etc)
3. Quadratic forms, symmetrization and contraction (Decoupling and symmetrization tricks etc)
4. Random processes (Slepian's, Sudakov's inequalities etc)