Mathematical Foundations of Data Science
Mathematische Grundlagen der Datenwissenschaft
8 CPWinterEN
Prerequisites
Recommended, as written
Good command of basic linear algebra, analysis and probability theory is recommended, e.g. as taught in the modules • 11103: Analysis I • 11104: Analysis II • 11101: Lineare Algebra und analytische Geometrie I • 11217: Wahrscheinlichkeitstheorie or 11917: Mathematik W-3 (Statistik) or 11212: Statistics
Contents
• Linear Regression • Empirical Risk Minimization • Model Assessment and Model Selection • Bias-Variance Decomposition • Bayesian Decision Theory • Naïve Bayes Classifier • Linear Classifiers
Learning outcomes
After completing the course, the students are able to apply statistical learning methods to justify conclusions drawn from data. They are familiar with fundamental properties, assumptions, limitations of the considered methods and their derivation.
Assessment
Prerequisite: • successful completion of a homework Final module examination: • written exam, 90 min.
Literature (3)
- Trevor Hastie, Robert Tibshirani, Jerome Friedman: The elements of statistical learning: data mining, inference, and prediction. Springer, 2009.
- Philippe Rigollet, Jan-Christian Hütter: High-Dimensional Statistics, Lecture Notes, MIT, 2023.
- Stefan Richter. Statistical analysis of machine learning algorithms, Lecture Notes, Universität Heidelberg, 2020.
Remarks
• Study programme Mathematical Data Science M.Sc.: Mandatory module • Study programme Mathematics M.Sc.: Compulsory elective module in complex „Stochastics“
Source: BTU's module description · retrieved 29 Sep 2026Original