High-Dimensional Statistics
Hochdimensionale Statistiken
8 CPirregularlyEN
Prerequisites
Recommended, as written
Knowledge of the content of the modules • 11103: Analysis I • 11104: Analysis II • 11101: Lineare Algebra und analytische Geometrie I • 11217: Wahrscheinlichkeitstheorie or very good knowledge of the content of the modules • 11113: Mathematics IT-2 (Linear Algebra) • 11213: Mathematics IT-3 (Analysis) • as well as of the content one of the modules - 11917: Mathematik W-3 (Statistik) - 11926: Statistik für Anwender - 11212: Statistics
Contents
Variety of the following topics: • Concentration of random vectors in high dimensions • Concentration inequalities • Linear and nonlinear principal component analysis (PCA) • Random matrices • Sparse recovery (compressed sensing) and LASSO regression • Introduction to statistical learning • Kernel methods and Gaussian processes • Applications in signal and image processing, random networks, …
Learning outcomes
After successfully completing the module, students have deepened their knowledge of stochastics acquired in the basic modules. They know the mathematical and statistical methods from data analysis. They have acquired basic skills for in-depth modules in stochastics or optimization. They also have experience in doing independent research.
Assessment
Prerequisite for Final Module Examination: • Successful completion of a semester project Final Module Examination: • Project presentation, 45 min.
Literature (4)
- C.M. Bishop. Pattern Recognition and Machine Learning. Springer, 2006.
- D.P. Dubhashi, A. Panconesi. Concentration of Measure for the Analysis of Randomized Algorithms, Cambridge University Press, 2009.
- R. van Handel. Probability in High Dimension. Lecture Notes, Princeton University, 2016.
- R. Vershynin. High-Dimensional Probability: An Introduction with Applications in Data Science, Cambridge University Press, 2018
Remarks
• Study programme Mathematics M.Sc.: Compulsory elective module in complex „Stochastics“ or in complex „Optimization“ • Study programme Mathematical Data Science M.Sc.: Compulsory elective module in complex „Advanced Mathematical Methods in Data Science“ • Study programme Mathematik B.Sc.: Compulsory elective module in complex „Specialisation“, in limited extend • Study programme Wirtschaftsmathematik B.Sc.: Compulsory elective module in complex „Specialisation“, in limited extend • Study programme Artificial Intelligence M.Sc.: Compulsory elective module in complex „Learning and Reasoning“ • Study programme Informatik B.Sc.: Compulsory elective module in „Applied Mathematics“ or in field of application „Mathematics“ • Study programme Informatik M.Sc.: Compulsory elective module in „Mathematics“ or in field of application „Mathematics“ • Study programme Physics M.Sc.: Compulsory elective module in complex „Minor Subject“
Source: BTU's module description · retrieved 29 Sep 2026Original