# 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, 11:15-13:00, HG E 33.5. The first lecture takes place on Thursday 29 Feb. 2024, 12:15-14:00, HG E 33.5. |

Discussion session: | Thursday, 13:15-14:00, HG E 33.5. The first discussion session takes place on Thursday 29 Feb. 2024, 11:15-12:00. |

Office hours: | Friday, 10:15-11:00 via Zoom. The first office hour takes place on Friday 01 Mar. 2024, 10:15-11:00. |

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 |

Teaching assistant: | Rodrigo Casado Noguerales |

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!

- On May 30. I will be available from 11:15 -- 13:00 in HG E 33.5 to answer questions to the lecture and the discussion session.
- There is no lecture and no discussion session on Feb. 22. We will find a replacement date for the first lecture.
- Problems 8 and 9 in the discussion session got swapped.
- From this year on, the exam will be oral.
- The time slots for lecture and discussion session got swapped.

#### 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: |

29.02.2024 | Problem 1 |

07.03.2024 | Problem 2 |

14.03.2024 | Problem 3 |

21.03.2024 | Problem 4 |

28.03.2024 | Problem 5 |

11.04.2024 | Problem 6 |

18.04.2024 | Problem 7 |

25.04.2024 | Problem 9 |

02.05.2024 | Problem 8 |

16.05.2024 | Problem 10 |

23.05.2024 | Problem 11 |

30.05.2024 | Problem 12 |

#### Previous years' exams and solutions

Summer Exam 2021: | Problems | Solutions | Handout |

Summer Exam 2022: | Problems | Solutions | Handout |

Summer Exam 2023: | Problems | Solutions | Handout |