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227-0434-10L 8 Credits DR , MSC D-ITET , D-MATH , D-INFK , D-PHYS
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Mathematics of Information

Lecturers & Examiners: Prof. Dr. Helmut Bölcskei
VVZ CR 4.0

Last Updated: 2026-02-05 16:23:00

Abstract

The class focuses on mathematical aspects of1. Information science: Sampling theorems, frame theory, compressed sensing, sparsity, super-resolution, spectrum-blind sampling, subspace algorithms, dimensionality reduction2. Learning theory: Approximation theory, greedy algorithms, uniform laws of large numbers, Rademacher complexity, Vapnik-Chervonenkis dimension

Objective

The aim of the class is to familiarize the students with the most commonly used mathematical theories in data science, high-dimensional data analysis, and learning theory. The class consists of the lecture and exercise sessions with homework problems.

Content

Mathematics of Information 1. Signal representations: Frame theory, wavelets, Gabor expansions, sampling theorems, density theorems 2. Sparsity and compressed sensing: Sparse linear models, uncertainty relations in sparse signal recovery, super-resolution, spectrum-blind sampling, subspace algorithms (ESPRIT), estimation in the high-dimensional noisy case, Lasso 3. Dimensionality reduction: Random projections, the Johnson-Lindenstrauss Lemma Mathematics of Learning 4. Approximation theory: Nonlinear approximation theory, best M-term approximation, greedy algorithms, fundamental limits on compressibility of signal classes, Kolmogorov-Tikhomirov epsilon-entropy of signal classes, optimal compression of signal classes 5. Uniform laws of large numbers: Rademacher complexity, Vapnik-Chervonenkis dimension, classes with polynomial discrimination

Resources

Lecture Notes

Detailed lecture notes will be provided at the beginning of the semester.

Learning Materials (Links)

General Information

Language
English
Levels
DR , MSC
Frequency
Yearly recurring

Examination

Type
session examination
Mode
written 180 minutes
Aids
10 handwritten or printed A4 pages summary (or 5 A4 pages on both sides). Electronic devices (laptops, calculators, cellphones, etc...) are not allowed.

Course Components

Type Title Time & Place Hours
lecture Mathematics of Information
  • Thu 09:15-12:00 (ML F 36)
  • 20.04 Date 08:15-12:00 (ML F 36)
3 h weekly
exercise Mathematics of Information
  • Mon 14:15-16:00 (ML E 12)
  • 20.03 Date 14:15-16:00 (ML D 28)
  • 27.03 Date 14:15-16:00 (ML D 28)
  • 03.04 Date 14:15-16:00 (ML D 28)
2 h weekly
independent project Mathematics of Information No time listed 2 h weekly

Offered In