Mathematics for Machine Learning

Module aims

In this module you will have the opportunity to study the advanced mathematical techniques required to understand, design and implement modern statistical machine learning algorithms and inference mechanisms.

Learning outcomes

Upon successful completion of this module you will be able to:

  • implement foundational machine learning algorithms from scratch
  • apply appropriate mathematical techniques in a machine learning setting
  • critically assess the quality of machine learning models
  • evaluate connections between different machine learning algorithms

Module syllabus

- Multivariate Calculus (einstein notation, differentiation and integration)
- Multivariate probability (joint pmfs, joint pdfs, means, covariance matrices)
- Conditional probability and Bayes's rule
- Maximum Likelihood estimation
- Monte Carlo Estimation
- Validation and test error estimation, and cross-validation
- Concentration inequalities (e.g. Law of Large Numbers)
- Gradient descent and its convergence
- PCA, eigendecomposition, SVD
- Bayesian inference
- MAP inference
- Multivariate Gaussians
- Bayesian Linear Regression

Recommended: The contents of COMP50008 Probability and Statistics.

Teaching methods

The material will be taught mostly through traditional lectures, backed up by unassessed problems designed to test your understanding of the material. There will be one or more assessed coursework exercises, possibly involving practical laboratory-based exercises.

An online web service will be used as an open online discussion forum for the module.


The assessed coursework contributes 30% of the marks for the module. There will be a final written exam, which counts for the remaining 70%.  

Written and verbal feedback will be provided throughout the module. Detailed written feedback will be provided on the coursework. Class-wide feedback will be provided after the exam.

Reading list

Core Reading

Supplementary Reading

Module leaders

Dr Yingzhen Li
Dr Mark van der Wilk