Machine Learning Theory

Fall 2018 (weeks 37 - 51). Lectures on Tuesday 10:15-13:00 at the UvA.

Aim | Prerequisites | Lecturers | Mode | Schedule | Material

Aim

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 and bandits.

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, forum discussions, and receiving grades.

Prerequisites

The only prerequisites are

all at the bachelor level. The course does require general 'mathematical maturity' though, 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.

Lecturers

Mode

The grade will be composed as follows.

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

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

Schedule

When What Who
Tue 11 Sep Introduction. Statistical learning. Halfspaces. Chapter 1 in [1]. Rianne
Tue 18 Sep PAC learnability for finite hyp. classes, realizable and agnostic cases. Uniform convergence. Chapters 2, 3 and 4 in [1]. Rianne
Tue 25 Sep Infinite classes. No Free Lunch. VC Dimension part 1. Chapters 5 and 6.1-6.3 in [1]. Rianne
Tue 2 Oct VC Dimendion part 2. Fundamental theorem of PAC learning. Sauer's Lemma. Chapter 6 in [1]. Rianne
Tue 9 Oct Proof of Fund.Th of PAC Learning. Nonuniform Learnability, SRM, Other notions of Learning. Chapter 7 in [1]. Rianne
Tue 16 Oct Rademacher Complexity. Chapters 26 in [1]. Peter
Tue 23 Oct Midterm exam.
Tue 30 Oct Full Information Online Learning (Experts). Wouter
Tue 6 Nov Bandits. UCB and EXP3. Chapters 2.2 and 3.1 in [3]. Wouter
Tue 13 Nov Non-stationary environments. Tracking. Wouter
Tue 20 Nov Online Convex Optimization, Sections 3.1 and 3.3 in [2]. Wouter
Tue 27 Nov Exp-concavity. Online Newton Step. Vovk mixability. Chapter 4 in [2]. Wouter
Tue 4 Dec Log-loss prediction. Normalised Maximum Likelihood. Non-parametric classes. Peter
Tue 11 Dec Boosting. AdaBoost. Chapter 10 in [1]. Wouter
Tue 18 Dec TBD Wouter
TBD Jan Final exam.

Material

We will make use of the following sources