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High-dimensional Statistics and Machine Learning
(dt. Hochdimensionale Statistik und maschinelles Lernen)

Level, degree of commitment Specialization module, depends on importing study program
Forms of teaching and learning,
workload		 Lecture (3 SWS), recitation class (1 SWS),
180 hours (60 h attendance, 120 h private study)
Credit points,
formal requirements		 6 CP
Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises.
Examination type: Written or oral examination (individual examination)
Language,
Grading		 English,
The grading is done with 0 to 15 points according to the examination regulations for the degree program M.Sc. Business Mathematics.
Origin M.Sc. Business Mathematics, M.Sc. Business Mathematics
Duration,
frequency		 One semester,
Regularly alternating with other specialization modules
Person in charge of the module's outline Prof. Dr. Hajo Holzmann

Contents

  • High-dimensional linear model and the LASSO.
  • High dimensional covariance matrix estimation.
  • Principal component analysis in high dimension
  • Multiple linear regression and matrix completion
  • Nonparametric least squares estimation, oracle inequalities, and neural networks
  • Fundamentals of classification and support vector machines

Qualification Goals

Translation is missing, sorry. German original:

Die Studierenden

  • können Theorien der aktuellen Forschungsgebiete der hochdimensionalen Statistik und des maschinellen Lernens erläutern,
  • können wichtige Algorithmen beschreiben und einsetzen und deren Funktionsweise in der Programmiersprache R erklären,
  • haben mathematische Arbeitsweisen (Entwickeln von mathematischer Intuition und deren formaler Begründung, Abstraktion, Beweisführung) vertieft,
  • haben in den Übungen ihre mündliche Kommunikationsfähigkeit durch Einüben der freien Rede vor einem Publikum und bei der Diskussion verbessert.

Prerequisites

None. The competences taught in the following modules are recommended: either Foundations of Mathematics and Linear Algebra I and Linear Algebra II or Basic Linear Algebra, either Analysis I and Analysis II or Basic Real Analysis, Elementary Probability and Statistics, Internship Stochastics, Statistics and Statistical Learning.


Applicability

The module can be attended at FB12 in study program(s)

  • B.Sc. Mathematics
  • B.Sc. Business Mathematics
  • M.Sc. Data Science
  • M.Sc. Mathematics
  • M.Sc. Business Mathematics

When studying M.Sc. Business Mathematics, this module can be attended in the study area Compulsory Elective Modules in Mathematics.

The module can also be used in other study programs (export module).


Recommended Reading

  • Wainwright, M. (2019) High-dimensional statistics: A non-asymptotic viewpoint. Cambridge University Press
  • Giraud, C. (2014) Introduction to high-dimensional statistics. CRC Press
  • Hastie, T., Tibshirani, R. und Wainwright, M. (2015) Statistical learning with sparsity: the lasso and generalizations. CRC Press



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2025/26. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

  • Winter 2016/17 (no corresponding element)
  • Summer 2018 (no corresponding element)
  • Winter 2018/19 (no corresponding element)
  • Winter 2019/20 (no corresponding element)
  • Winter 2020/21 (no corresponding element)
  • Summer 2021 (no corresponding element)
  • Winter 2021/22 (no corresponding element)
  • Winter 2022/23 (no corresponding element)
  • Winter 2023/24
  • Winter 2025/26

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.