Spring 2021 (weeks 6 - 21). Lectures on Thursday 10:15-13:00 held online.
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 Zulip MLTs21 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 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.
When | What | Lect. | TA |
Thu 11 Feb | Introduction. Statistical learning. Halfspaces. PAC learnability for finite hyp. classes, realizable case. Chapters 1 and 2 in [1] | Tim | N/A |
Thu 18 Feb | PAC learnability for finite hyp. classes, agnostic case. Uniform convergence. Chapters 3 and 4 in [1]. | Tim | Jack |
Thu 25 Feb | Infinite classes. VC Dimension part 1. Chapter 6.1-6.3 in [1]. | Tim | Sarah |
Thu 4 Mar | VC Dimendion part 2. Fundamental theorem of PAC learning. Sauer's Lemma. Chapter 6 in [1]. | Tim | Hédi |
Thu 11 Mar | Proof of Fund.Th of PAC Learning. Nonuniform Learnability, SRM, Other notions of Learning. Chapter 7 in [1]. | Tim | Jack |
Thu 18 Mar | Rademacher Complexity. Chapter 26 in [1]. | Tim | Sarah |
Thu 25 Mar | Double descent. Generalisation despite zero training loss | Tim | Hédi |
Thu 1 Apr | Midterm exam | ||
Thu 8 Apr | Full Information Online Learning (Experts). | Wouter | Jack |
Thu 15 Apr | Bandits. UCB and EXP3. Chapters 2.2 and 3.1 in [3] | Wouter | Sarah |
Thu 22 Apr | Online Convex Optimization. Sections 3.1 and 3.3 in [2] | Wouter | Hédi |
Thu 29 Apr | Exp-concavity. Online Newton Step. | Wouter | Jack |
Thu 6 May | Boosting. AdaBoost. Margin theory. Chapter 10 in [1] | Wouter | Sarah |
Thu 13 May | Log-loss prediction. Normalised Maximum Likelihood. Non-parametric classes | Wouter | Hédi |
Thu 20 May | Reinforcement Learning | Wouter | Jack |
Thu 27 May | Bonus (topic tbd) | Wouter | Sarah |
Thu 10 Jun | Final exam | ||
Thu 1 Jul | Retake exam(s) |
The dependency graph of the online learning component of the course
We will make use of the following sources