Mathematics for Machine Learning
Course: Winter Semester 2021
Prof. Dr. Gerard Pons-Moll
Continuous Learning of Multimodal Data Streams
University of Tuebingen
ATTENDANCE REGISTRATION
Please fill out this form before attending the first lecture. Pre-registration is mandatory for lecture attendance. We only have 60 spots availabe. The portal will close once all the slots are taken.Description
This course is intended for master students who plan to dive further in machine learning. Depending on your background, much of the material might be a recap - or not. Contents of the course are Linear algebra, Mulitvariate analysis, Probability Theory, Statistics, Optimization. Tentatively, the following topics will be covered in the course:- Linear Algebra
- Multivariate Calculus
- Optimization
- Probability and Statistics
- Phenomena in high dimensions
- Approximation Theory and Functional Analysis
Organization
This course is worth 9 ECTS points. Lectures will be delivered every week by Prof. Gerard Pons-Moll. Lectures will be delivered in person on Tuesday between 1200 and 1400. and on Wednesday between 0800 and 1000. Lectures will be recoreded and uploaded on moodle as well.All lectures will be delivered in the main lecture hall of Maria von Linden Strasse 6, 72076 Tübingen. Due to covid, we will have to limit the number of participants to roughly 60. To attend you need to present proof of vaccination or recovery, or a negative corona test. The lecture will also be available via zoom. The zoom link will be made available in Moodle.
There will be two weekly tutorials as well - on Thursday between 1200 and 1400 in Lecture Hall A301 (Sand 1) and on Friday between 1000 and 1200 in Lecture Hall 1 F119 (Sand 6/7). To attend a tutorial, you need to present proof of vaccination or recovery, or a negative corona test. The TAs for the course are:
Assignments
There will be weekly assignments that you have to solve in groups of three students. Achieving half of the possible points is a formal requirement for being admitted to the exam. This is a purely theoretical course and all assignments will be theoretical in nature.Exam
The final exams will take place on-site in Tuebingen, and you need to be physically present. There is going to be one exam at the beginning of the semester break and one at the end of the semester break. The general mode for exams is: You are not allowed to bring any material (books, slides, etc) except for what we call the controlled cheat sheet: one side (A4, one side only) of handwritten (!) notes, made by yourself. This cheat sheet has to be handed in together with the exam.Course Content
Lecture slides and assignment sheets will be distributed via moodleSchedule
Date | No. | Title | Exercise | |
Tu. 19.10. | L1 | Linear Algebra 1 - Linear Systems | ||
We. 20.10. | L2 | Linear Algebra 2 - Determinants | ||
Tu. 26.10. | L3 | Linear Algebra 3 - Eigenvalues | ||
We. 27.10. | L4 | Linear Algebra 4 - Eigenvalues and Eigenvectors | Ex01 Out | |
Tu. 02.11. | L5 | Linear Algebra 5 - Rayleigh Qutient | Ex01 Due | |
We. 03.11. | L6 | Linear Algebra 6 - Metric Spaces | Ex02 Out | |
Tu. 09.11. | L7 | Linear Algebra 7 - Low Rank Approximations | Ex02 Due | |
We. 10.11. | No Lecture | |||
Tu. 16.11. | L8 | Calculus 1 - Convergence, Continuity and Derivatives | Ex03 Due Ex04 Out | |
We. 17.11. | L9 | Calculus 2 - Local Extrema | ||
Tu. 23.11. | L10 | Optimization 1 - Introduction | ||
We. 24.11. | L11 | Optimization | Ex04 Due Ex05 Out | |
Tu. 30.11. | L12 | Optimization | ||
We. 01.12. | No Lecture | Ex05 Due Ex06 Out | ||
Tu. 07.12. | L13 | Optimization | ||
We. 08.12. | L14 | Optimization | Ex06 Due Ex07 Out | |
Tu. 14.12. | L15 | Optimization | ||
We. 15.12. | L16 | Optimization | Ex07 Due Ex08 Out | |
Tu. 21.12. | L17 | Probability | ||
We. 22.12. | L18 | Probability | Ex08 Due Ex09 Out | |
Tu. 11.01. | L19 | Probability | ||
We. 12.01. | L20 | Probability | Ex09 Due Ex10 Out | |
Tu. 18.01. | L21 | Probability | ||
We. 19.01. | L22 | Statistics | Ex10 Due Ex11 Out | |
Tu. 25.01. | L23 | Statistics | ||
We. 26.01. | L24 | Statistics | Ex11 Due Ex12 out | |
Tu. 01.02. | L25 | Open Questions | ||
We. 02.02 | L26 | Open Questions | Ex12 Due |
Literature:
To go a bit deeper into the topics we cover in this course, the following textbooks are ideal.- Deisenroth, Faisal, Ong:Mathematics for Machine Learning
- Sheldon Axler: Linear Algebra Done Right.
- Charles Pugh: Real Mathematical Analysis
- Terence Tao: Analysis 1 and 2.
- Walter Rudin: Principles of Mathematical Analysis.
- Jacod Protter: Probability essentials.
- Larry Wasserman: All of statistics