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Bayesian Uncertainty Quantification for Clustering Problems

School of Mathematical Sciences

, Tuesday, January 26, 2021 Competition Funded PhD Project (Students Worldwide)

About the Project

The School of Mathematical Sciences of Queen Mary University of London invite applications for a PhD project commencing in September 2021.

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 . This project is eligible for full funding, including support for 3.5 years’ study, additional funds for conference and research visits and funding for relevant IT needs. Applicants interested in the full funding will have to participate in a highly competitive selection process.

Funding Notes

For September 2021 entry: Funding may be available through QMUL Principal's Postgraduate Research Studentships, School of Mathematical Sciences Studentships, and EPSRC DTP, in competition with all other PhD applications.

Studentships will cover tuition fees, and a stipend at standard rates for 3-3.5 years.

We welcome applications for self-funded applicants year-round, for a January, April or September start.

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.

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