Spring 2025 (weeks 6 - 21). Lectures on Thursday 14:00-16:45 at the UvA, room TBA.
Machine learning is one of the fastest growing areas of science, with far-reaching applications. In this course we focus on the fundamental ideas, theoretical frameworks, and rich array of mathematical tools and techniques that power machine learning. The course covers the core paradigms and results in machine learning theory with a mix of probability and statistics, combinatorics, information theory, optimization and game theory.
During the course you will learn to
This course strongly focuses on theory. (Good applied master level courses on machine learning are widely available, for example here, here and here). We will cover statistical learning theory including PAC learning, VC dimension, Rademacher complexity and Boosting, as well as online learning including prediction with expert advice, online convex optimisation, bandits and reinforcement learning.
This course is offered as part of the MasterMath program. To participate for credit, sign up here. We use the MasterMath ELO for submitting homework, and receiving grades.
We use the MasterMath ELO for announcements and as our student forum.
The prerequisites are
as covered e.g. in any bachelor mathematics program in the Netherlands, and as reviewed in the Appendix of the book [1]. The course does require general 'mathematical maturity', in particular the ability to combine insights from all three fields when proving theorems.
We offer weekly homework sets whose solution requires constructing proofs. This course will not include any programming or data.
The lectures will be held on location at the UvA, room TBD.
The Thursday 3h slot will consist of 2h of lectures followed by a 1h TA session discussing the homework.
We provide weekly homework sets. Odd sets are graded and must be handed in before the next lecture. Even sets are for practice.
The grade will be composed as follows.
The average of midterm and final exam grades has to be at least 5.0 to pass the course.
There will be a retake possibility for either or both exams, which are 70% of the grade. The homework still counts as part of the grade after the retake.
It is allowed and strongly encouraged to solve and submit the homework in small teams. Exams are personal.
NB Collaboration on homework is only allowed within a team. In particular, solutions may
When using any source that is not on the official literature list, always cite the source.
| Wk | When | What | Lect. | TA |
| 6 | Thu 6 Feb | Introduction. Statistical learning. Halfspaces. PAC learnability for finite hyp. classes, realizable case. Chapters 1 and 2 in [1]. | Tim | N/A |
| 7 | Thu 13 Feb | PAC learnability for finite hyp. classes, agnostic case. Uniform convergence. Chapters 3 and 4 in [1]. | Tim | Roy |
| 8 | Thu 20 Feb | Infinite classes. VC Dimension part 1. Chapter 6.1-6.3 in [1]. | Tim | Roy |
| 9 | Thu 27 Feb | VC Dimension part 2. Fundamental theorem of PAC learning. Sauer's Lemma. Chapter 6 in [1]. | Recorded lecture | Roy |
| 10 | Thu 6 Mar | Proof of Fund.Th of PAC Learning. Rademacher Complexity part 1. Section 28.1 in [1]. | Tim | Roy |
| 11 | Thu 13 Mar | No lecture (Wouter's Inaugural Address) | ||
| 12 | Thu 20 Mar | Nonuniform Learnability, SRM, Other notions of Learning. Sections 7.1 and 7.2 in [1] (note the errata about this chapter). Rademacher Complexity part 2. Chapter 26 in [1]. | Tim | Roy |
| 13 | Thu 27 Mar | Midterm exam on material covered in lectures 1-6. | ||
| 14 | Thu 3 Apr | Generalisation of deep neural networks. Double descent. This material is not part of either exam. | Tim | Roy |
| 15 | Thu 10 Apr | Full Information Online Learning (Experts). | Wouter | Roy |
| 16 | Thu 17 Apr | Bandits. UCB and EXP3. | Wouter | Roy |
| 17 | Thu 24 Apr | Online Convex Optimization. | Wouter | Roy |
| 18 | Thu 1 May | Exp-concavity. Online Newton Step. | Wouter | Roy |
| 19 | Thu 8 May | Boosting. AdaBoost. and Chapter 10 in [1]. | Wouter | Roy |
| 20 | Thu 15 May | Log-loss prediction. Normalised Maximum Likelihood. book chapter on ELO. | Wouter | Roy |
| 21 | Thu 22 May | Part 2 special topic. This material is not part of either exam | Wouter | Roy |
| 24 | Thu 12 Jun | Final exam | ||
| 27 | Thu 3 Jul | Retake exam(s) |
The first half of the course will use the book
The second half of the course will use slides posted above and on the ELO.
Consult these references to learn more