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Bayesian Uncertainty Quantification for Clustering Problems

Project Description

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing either in September 2019 for students seeking funding, or at any point in the academic year for self-funded students. The deadline for funded applications was 14 January 2019 (if you wish to be considered for the Alan Turing Institute studentship) or 31 January 2019 for all other funded studentships.

This project will be supervised by Dr. Williamo Yoo and Dr. Silvia Liverani.

Clustering is widely used in statistics and machine learning. In clustering, we try to group data that are similar or are close to each other to form different groups we call clusters. Dividing up the data into different clusters tells us a lot about the structure of the data and it has many applications, such as detecting galaxy clusters in astronomy, identifying communities in a social network, dividing pixels into distinct regions for border detection and object recognition.

Many clustering methods and algorithms have been proposed in the literature. Canonical examples include k-means clustering and the hierarchical Dirichlet process. Most of these methods deal with point estimate of the clusters, where one single arrangement of the clusters is deemed the best under some loss criterion. However, methods to assess the quality and the associated uncertainty of this estimate are far less explored in the literature.

Therefore, this project will investigate Bayesian uncertainty quantification for clustering, and in particular to develop the theory and methodology needed in order to build credible sets for clusters with good properties. We use the Bayesian approach because other than point estimates, it also gives estimates of uncertainty automatically once we have the posterior distribution. However, Bayesian computation is very demanding and does not scale very well with the dimension of the data, hence another important component of this project is to develop new clustering algorithms or techniques to deal with high-dimensional data.

The methods developed during this PhD will be applied to suitable datasets, such as data from environmental epidemiology and biology.

The application procedure is described on the School website. For further inquiries please contact Dr William Yoo or Dr. Silvia Liverani .

Funding Notes

The project can be undertaken as a self-funded project, either through your own funds or through a body external to Queen Mary University of London. Self-funded applications are accepted year-round.

The School of Mathematical Sciences is committed to the equality of opportunities and to advancing women’s careers. As holders of a Bronze Athena SWAN award we offer family friendly benefits and support part-time study. Further information is available here. We strongly encourage applications from women as they are underrepresented within the School.

We particularly welcome applicants through the China Scholarship Council Scheme.

Related Subjects

How good is research at Queen Mary University of London in Mathematical Sciences?

FTE Category A staff submitted: 34.80

Research output data provided by the Research Excellence Framework (REF)

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