MMath Mathematics

An introduction to machine learning models and algorithms, both for unsupervised and supervised learning, with a focus on the underlying mathematical and statistical principles, while including some aspects of implementation and practice. Studying the relation of machine learning approaches with traditional statistical methods. 

One of either MATH38161 Multivariate Statistics and Machine Learning or MATH48061 Multivariate Statistics required as a pre-requisite.

The unit aims to:

Provide an introduction to machine learning models and algorithms, both for unsupervised and supervised learning, with a focus on the underlying mathematical and statistical principles, while including some aspects of implementation and practice.  A further aim is to study the relation of machine learning approaches with traditional statistical methods. 

On the successful completion of the course, students will be able to:

1. Explain the principles underlying both probabilistic and algorithmic machine learning techniques
2. Select and identify appropriate methodology for data analysis at the interface of statistics and machine learning
3. Apply modern machine learning methods to supervised and unsupervised learning problems
4. Use R and/or Python to analyse data with the methods discussed in the course

Part A - Nonlinear (non-neural network) machine learning approaches

• Limitations of traditional linear statistical models
• Supervised Machine Learning:

      -   K-nearest neighbours (including Bayesian KNN)

      -   Decision trees and random forests

• Unsupervised Machine Learning:

      -   Nonparametric clustering (e.g. Dirichlet process mixture models)

      -   Topic models (e.g. Latent Dirichlet Allocation)

      -   Dimensionality reduction including manifold learning (SNE, t-SNE)

Part B - Nonlinear (neural network) machine learning approaches

• Single-layer neural networks and deep neural networks
• Optimising neural networks (gradient descent, backpropagation)
• Statistical properties (overparametrisation, regularisation, universal function approximation)
• Standard models (e.g. multi-layer perceptron, convolutional networks, auto-encoders) and diverse data types (e.g. image data, time series, text data) 

Teaching is composed of two hours of lectures per week and one tutorial class per week. Teaching materials will be made available online for reference and review. One week is reserved for coursework.

Other = coursework data analysis project, with a 30% weighting

Generic feedback will be provided after marks are released. 

C. M. Bishop and H. Bishop. 2024.  Deep learning: Foundations and concepts. Springer.

https://link.springer.com/book/10.1007/978-3-031-45468-4  

G. James et al. 2021. An introduction to statistical learning with applications in R (2nd edition). Springer.

https://link.springer.com/book/10.1007/978-1-0716-1418-1  

G. James et al. 2023. An introduction to statistical learning with applications in Python. Springer.

https://link.springer.com/book/10.1007/978-3-031-38747-0  

https://www.statlearning.com/  

K. P. Murphy. 2022. Probabilistic machine learning: An introduction. MIT Press.

https://mitpress.mit.edu/9780262046824/probabilistic-machine-learning/  

https://probml.github.io/pml-book/book1.html  

A. Zhang et al. 2024. Dive into deep learning. Cambridge University Press.

https://d2l.ai/