Machine Learning Theory

Spring 2022 (weeks 6 - 21). Lectures on Thursday 10:15-13:00.

Aim | Prerequisites | Lecturers | Mode | Schedule | Exams | Material


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.

MasterMath Website

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 Zulip MLTs22 stream as our forum. Sign up instructions are here.


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 VU, room WN M143. To view them remotely, join the zoom live stream. Mastermath has kindly offered us recording support. Recorded lectures will be posted to our vimeo archive.

The Thursday 3h slot will consist of 2h of lectures followed by a 1h TA session discussing the homework.


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.

It is strongly encouraged to solve and submit your weekly homework in small teams. Exams are personal.

There will be a retake possibility for either/both exams, which are 60% of the grade.

Preliminary Schedule

When What Lect. TA
Thu 10 Feb Introduction. Statistical learning. Halfspaces. PAC learnability for finite hyp. classes, realizable case. Chapters 1 and 2 in [1]. Slides Tim N/A
Thu 17 Feb PAC learnability for finite hyp. classes, agnostic case. Uniform convergence. Chapters 3 and 4 in [1]. Slides Tim Sarah
Thu 24 Feb Infinite classes. VC Dimension part 1. Chapter 6.1-6.3 in [1]. Slides Tim Sarah
Thu 3 Mar VC Dimendion part 2. Fundamental theorem of PAC learning. Sauer's Lemma. Chapter 6 in [1]. Slides Tim Sarah
Thu 10 Mar Proof of Fund.Th of PAC Learning. Rademacher Complexity part 1. Section 28.1 in [1]. Slides Tim Hédi
Thu 17 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]. Slides Tim Hédi
Thu 24 Mar Generalisation of deep neural networks. Double descent. This material is not part of either exam. Slides Tim Hédi
Thu 31 Mar Midterm exam on material covered in lectures 1-6.
Thu 7 Apr Full Information Online Learning (Experts). Slides Wouter Hédi
Thu 14 Apr Bandits. UCB and EXP3. Slides and Chapters 2.2 and 3.1 in [3]. Wouter Sarah
Thu 21 Apr Online Convex Optimization. Slides and Sections 3.1 and 3.3 in [2]. Wouter Hédi
Thu 28 Apr Exp-concavity. Online Newton Step. Slides and Chapter 4 in [2]. Wouter Sarah
Thu 5 May Holiday (Liberation Day)
Thu 12 May Boosting. AdaBoost. Slides and Chapter 10 in [1]. Wouter Sarah
Thu 19 May Log-loss prediction. Normalised Maximum Likelihood. Slides and book chapter on ELO. Wouter Hédi
Thu 23 Jun Final exam
Thu 14 Jul Retake exam(s)


We will make use of the following sources