Machine learning studies automatic methods for identifying patterns in complex data and for making predictions based on past observations. In this course, we develop rigorous mathematical foundations of machine learning, in order to provide guarantees about the behaviour of learning algorithms and also to understand the inherent difficulty of learning problems.

The course will begin by providing a statistical and computational toolkit, such as concentration inequalities, fundamental algorithms and methods to analyse learning algorithms. We will cover questions such as when can we generalise well from limited amounts of data, how can we develop algorithms that are compuationally efficient, and understand statistical and computational trade-offs in learning algorithms. We will also discuss new models designed to address relevant practical questions of the day, such as learning with limited memory, communication, privacy, and labelled and unlabelled data. In addition to core concepts from machine learning, we will make connections to principal ideas from information theory, game theory and optimisation.

This is an advanced course requiring a high level of mathematical maturity. It is expected that students will have taken prior courses on algorithms and complexity. A formal course on Machine Learning is not required, however, students are more likely to appreciate the contents of the course if they have some familiarity with machine learning.


There are no hard pre-requisites for this course. However, if you have not taken a majority of the following courses at Oxford (or their equivalents elsewhere), you will find the course challenging.

Who should take this course?

This course is open to Part C students in Computer Science, Computer Science and Philosophy, Mathematics and Computer Science, and Mathematics and Philosophy, as well as MSc students in Computer Science and Mathematics and Foundations of Computer Science. This course covers fundamental algorithmic, computational and mathematical ideas behind machine learning. Students interested in practical applications should consider other more applied courses such as Machine Learning or Advanced Machine Learning.

Note: Anybody who holds a University of Oxford Bod Card is welcome to attend lectures and view the materials posted on the website; there is no need to email the course lecturer to confirm. However, the classes are only for officially registered students. Registration is only allowed for students in programs listed in the official handbook.


The first half of the course will closely follow the following introductory text. However, in order to deepen your understanding you will need to refer to additional text and primary literature.

  • Michael Kearns and Umesh Vazirani. An Introduction to Computational Learning Theory. MIT Press, 1994.

Additional Reading

  • Mehryar Mohri, Afshin Rostamizadeh and Amit Talwar. Foundations of Machine Learning. MIT Press, 2012.
  • Shai Shalev-Shwartz and Shai Ben-David. Understanding Machine Learning: From Theory to Algorithms. Cambridge University Press, 2014.
  • Vladimir Vapnik. The nature of Statistical Learning Theory. Springer 1999.
  • Alexandre B. Tsybakov. Introduction to Nonparametric Estimation. Springer 2009.
  • Edwin T. Jaynes. Probability Theory: The logic of science. Cambridge University Press, 2003.
  • David Mackay. Information Theory, Inference and Learning Algorithms. Cambridge University Press, 2003.


There will be a take-home examination for this course. The exact dates and locations for pick-up and hand-in may differ depending on the programme you are enrolled in, and will be announced in the middle of the term. You will be required to typeset your answers, preferably using LaTeX; using LaTeX to typset your solutions to problem sheets will help you practice. Where necessary, use of scanned pictures drawn by hand will be acceptable, but equations must be typed. Page limits on the examination guidelines will be strictly enforced, so you must practice writing succinctly.

Contact Information

Apart from lectures and classes, we have set up a Piazza forum. Please sign up here. You should use this forum to ask questions which could be answered by your classmates, TAs, and the lecturer. Should you so wish, you can also post to this forum anonymously. You may also send private messages to the lecturer and teaching staff, though we recommend that you use this option sparingly.

If your question is personal in nature, you should contact the lecturer and/or your academic superviser/adviser directly via email. Please allow at least 48 hours for an email response.

It can be challenging for the lecturer to gauge how smoothly the course is progressing. Your comments, suggestions and feedback are always welcome. If you would like to remain anonymous while doing so, feel free to use an anonymous emailer such as this one. In addition, please do not forget to fill out the official feedback forms at the end of the term.