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 a mathematical course that with several definitions, theorems and proofs. It is expected that students will have some familiarity with probability, algorithms, and basic 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, it would be helpful if you have taken a majority of the following courses at Oxford (or their equivalents elsewhere). You may need to do some extra reading to fill in gaps.

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 students enrolled in MSc in Advanced Computer Science, MSc in Mathematics and Foundations of Computer Science (MFoCS), and DPhil in Computer Science. This course covers fundamental algorithmic, computational and mathematical ideas behind machine learning. Part C students in Mathematics and Computer Science may also be interested in Algorithmic Foundations of Machine Learning and C6.5 Theories of Deep Learning which will suitably complement material taught in this course. Students interested in practical applications should consider other more applied courses such as Machine Learning or Geometric Deep Learning.


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 texts 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. You will be required to typeset your answers, preferably using LaTeX; using LaTeX to typset your solutions to problem sheets will help you practice for the exam. Where necessary, use of scanned pictures drawn by hand will be acceptable, but equations and text must be typed. Page limits on the examination guidelines will be strictly enforced, so you must practice writing succinctly.

Contact Information

For very brief questions, you can get in touch with the lecturer right after lectures. For more detailed questions please make use of the office hours announced on the course website.

We have set up a piazza forum. We hope you will make use of this to post questions, answer questions posted by your classmates, and generally make good use of this as a discussion forum. The lecturer will monitor the forum and answer questions as well. The option to post anonymously is enabled, should you wish to remain anonymous. Posting your question on this forum will allow other students to benefit from the answers.

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 or this one. In addition, please do not forget to fill out the official feedback forms at the end of the term.