Bayesian Cluster Analysis

Clustering is widely studied in statistics and machine learning, with applications in a variety of fields. However, an important problem, common to all clustering methods, is how to choose the number of clusters. In popular algorithms such as agglomerative hierarchical clustering or k- means, the number of clusters is fixed or selected based on specified criteria and a single clustering solution is returned. On the other hand, Bayesian model-based clustering provides a formal framework to assess uncertainty in the cluster structure and the number of clusters through the posterior over the space of partitions. Bayesian approaches to incorporate uncertainty in the number of clusters include 1) hierarchical approaches that include a prior over the number of clusters, 2) sparse overfitted mixtures that automatically prune unnecessary components, and 3) nonparametric infinite mixtures. This project will focus on empirical and theoretical comparisons of Bayesian models for cluster analysis, as well as the development of innovative algorithms for inference.

Entry requirements:

Essential:

• A Bachelor’s degree in Statistics, Mathematics, Physics, Computer Science or similar (a First Class or good Upper Second Class Honours degree, or the equivalent from an overseas university);

• Strong mathematical background and programming skills

• Strong verbal and written communication skills in English.

Desirable:

• Knowledge of Bayesian methods

Application Procedure:

A formal application for this project can be made here: https://www.ed.ac.uk/studying/postgraduate/degrees/index.php?r=site/view&edition=2020&id=516

You are advised to contact the supervisor before applying, although this is not essential.