Learning, Classification, and Compression
Offered in:
- Data Science Master: Wählbare Kernfächer
- Doktorat Departement Informationstechnologie und Elektrotechnik: Lehrangebot Doktorat und Postdoktorat
- Elektrotechnik und Informationstechnologie Master: Vertiefungsfächer
- Elektrotechnik und Informationstechnologie Master: Empfohlene Fächer
- Mathematik Bachelor: Auswahl: Weitere Gebiete
- Mathematik Master: Auswahl: Weitere Gebiete
- Physik Master: Allgemeine Wahlfächer
- Statistik Master: Statistische und mathematische Fächer
- Statistik Master: Fachbezogene Wahlfächer
Basic Information:
| Lecture: | Thursday, 12:15-14:00, HG E 33.5. The first lecture takes place on Thursday 27 Feb. 2025, 11:15-13:00, HG E 33.5. |
| Discussion session: | Thursday, 11:15-12:00, HG E 33.5. The first discussion session takes place on Thursday 27 Feb. 2025, 13:15-14:00. |
| Office hours: | Friday, 14:15-15:00 via Zoom. The first office hour takes place on Friday 28 Feb. 2025, 14:15-15:00. |
| Zoom Links: | The Zoom link for the office hours can be found at this page (access credentials are the same as for the lecture/exercise notes). |
| Instructor: | Dr. Erwin Riegler |
| Lecture notes: | Detailed lecture notes will be made available as we go along. |
| Prerequisites: | This course is aimed at students with a solid background in measure theory and linear algebra and basic knowledge in functional analysis. |
| Credits: | 4 ECTS credits. |
| Course structure: | The class will be taught in English. There will be an oral exam of duration 30 minutes. |
Course Information:
The focus of the course is aligned to a theoretical approach of learning theory and classification and an introduction to lossy and lossless compression for general sets and measures. We will mainly focus on a probabilistic approach, where an underlying distribution must be learned/compressed. The concepts acquired in the course are of broad and general interest in data sciences.
After attending this lecture and participating in the exercise sessions, students will have acquired a working knowledge of learning theory, classification, and compression.
News
We will post important announcements, links, and other information here in the course of the semester, so please check back often!
- There is no lecture and no discussion session on Feb. 20. We will find a replacement date for the first lecture.
- Starting from 6.3.2025, the lecture will be from 12:15-14:00.
- The office hours will be on Friday 14:15-15:00.
- The discussion session and the office hour will be on demand. Please write me an email until Wednesday 12:00 if you want to attend the discussion session or the office hour.
- The lecture on 22.05.2025 is canceled! Please watch the video from 01.06.2022 at this page starting from 38:30. The login for the videos is: Login: rie-22s Passwort: r6h7VT4
Content of the Course:
- Learning Theory:
- Framework of Learning
- Hypothesis Spaces and Target Functions
- Reproducing Kernel Hilbert Spaces
- Bias-Variance Tradeoff
- Estimation of Sample and Approximation Error
- Classification:
- Binary Classifier
- Support Vector Machines (separable case)
- Support Vector Machines (nonseparable case)
- Kernel Trick
- Lossy and Lossless Compression:
- Basics of Compression
- Compressed Sensing for General Sets and Measures
- Quantization and Rate Distortion Theory for General Sets and Measures
Prerequisites
This course is aimed at students with a solid background in measure theory and linear algebra and basic knowledge in functional analysis.
Lecture Notes and problems+solutions:
- Lecture Notes Part I - Learning and Classification (Version 24.08.2022)
- Problems + Solutions (Version 24.08.2022)
- Slides on Lossy Compression
Problem sets and solutions
There will be several problem sets for this course, which will help you better understand the lectures and prepare you for the exam (See download link Problems + Solutions above). The following problem will be discussed in the discussion session:
| Discussion Session: | Problem: |
| 27.02.2025 | Problem 1 |
| 06.03.2025 | Problem 2 |
| 13.03.2025 | Problem 3 |
| 20.03.2025 | Problem 4 |
| 27.03.2025 | Problem 5 |
| 03.04.2025 | Problem 6 |
| 10.04.2025 | Problem 7 |
| 17.04.2025 | Problem 8 |
| 08.05.2025 | Problem 9 |
| 15.05.2025 | Problem 10 |
| 22.05.2025 | Problem 11 |
Parts of the notes relevant for the exam:
- Lecture notes: The appendices and the addendum are excluded. Required results from the addendum will be provided via handouts at the exam.
- All problem sets.
- The slides on lossy compression are excluded.
Note that you are not required to learn proofs by heart or to recite key steps in proofs. You are, however, expected to understand the main ideas/techniques/concepts used in the proofs in the relevant material listed above.
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Previous years' exams and solutions
| Summer Exam 2021: | Problems | Solutions | Handout |
| Summer Exam 2022: | Problems | Solutions | Handout |
| Summer Exam 2023: | Problems | Solutions | Handout |