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Module Number:
| 14114
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| Module Title: | High-Dimensional Statistics |
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Hochdimensionale Statistiken
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| Department: |
Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
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| Responsible Staff Member: | -
Prof. Dr. rer. nat. Hartmann, Carsten
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| Language of Teaching / Examination: | English |
| Duration: | 1 semester |
| Frequency of Offer: |
On special announcement
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| Credits: |
8
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| Learning Outcome: | 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. |
| 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, …
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| Recommended Prerequisites: | 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
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| Mandatory Prerequisites: | None |
| Forms of Teaching and Proportion: | -
Lecture
/ 4 Hours per Week per Semester
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Exercise
/ 2 Hours per Week per Semester
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Self organised studies
/ 150 Hours
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| Teaching Materials and Literature: | - 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
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| Module Examination: | Prerequisite + Final Module Examination (MAP) |
| Assessment Mode for Module Examination: | Prerequisite for Final Module Examination:
- Successful completion of a semester project
Final Module Examination:
- Project presentation, 45 min.
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| Evaluation of Module Examination: | Performance Verification – graded |
| Limited Number of Participants: | None |
| Part of the Study Programme: | -
Master (research-oriented) /
Mathematical Data Science /
PO 2025
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| 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“
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| Module Components: | - Lecture: High-Dimensional Statistics
- Accompanying exercise
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| Components to be offered in the Current Semester: | |
