About the Project
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 email@example.com or Dr. Silvia Liverani firstname.lastname@example.org. 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.
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.
Why not add a message here
Based on your current searches we recommend the following search filters.
Based on your current search criteria we thought you might be interested in these.