EPSRC DTP studentships at Cardiff’s School of Mathematics

Cardiff’s School of Mathematics invites applications for:

Two EPSRC DTP studentships
at the interface of Statistics, Analysis and Machine Learning

Project (1): Spectral approximation of extremal dependence in high dimensions
Project (2): Sparsity and structures in large-scale machine learning problems
(Descriptions below)

The School provides an excellent postgraduate research environment. The latest PRES ranks its overall satisfaction 3rd and its professional development 1st (out of 22). The training in these projects opens up outstanding career prospects both in academia and industry.

Each 3.5 year studentship includes fees, stipend and RTSG. The stipend and fees are at the UKRI rate (for 2020/21 is £15,285; £4,407 respectively). The Research Training Support Grant is a total of £4,000 to cover costs such as research consumables, training, conferences and travel.

HOW TO APPLY

Applicants should apply through the Cardiff University online application portal for a Doctor of Philosophy in Mathematics with an entry point of October 2020:

https://www.cardiff.ac.uk/study/postgraduate/research/programmes/programme/mathematics

In the research proposal section of your application, please specify the project title and supervisors of this project. In the funding section, please select “I will be applying for a scholarship / grant” and specify that you are applying for advertised funding from EPRSC DTP.

Administrative enquiries:
PGR Office Mathematics: maths-pgr@cardiff.ac.uk
Project-specific enquiries:
Dr Kirstin Strokorb: StrokorbK@cardiff.ac.uk
Dr Bertrand Gauthier: GauthierB@cardiff.ac.uk

Closing Date: 16 March 2020.
Shortlisted candidates will be invited to attend an interview in April.

ELIGIBILITY CRITERIA

UK/EU applicants only. UK Research Council eligibility conditions apply.

A 1st or upper 2nd class UK Honours degree (or equivalent) and/or a Master’s degree is required in mathematics or a related subject. Applicants for whom English is not their first language must demonstrate their proficiency by obtaining an IELTS score of at least 6.5 overall, with a minimum of 5.5 in each skills component.

STUDENTSHIP DESCRIPTIONS

Project (1): Spectral approximation of extremal dependence in high dimensions

This studentship will develop novel tools for assessing extremal dependence in high dimensions. It is based on extending a recently discovered link between classical principal component analysis and multivariate extreme value theory.

While most statistical tools that have a strong theoretical underpinning characterise the typical behaviour of a system, in many practical or safety-critical situations it is instead the extreme behaviours and their dependence, which require particular attention. Contrary to public perception, examples of such settings are ubiquitous and an improved understanding aided by sound statistical procedures is of utmost importance, for instance to assess risk related to environmental hazards, network failure or financial portfolio losses. What complicates such tasks is the lack of generic and interpretable, theoretically well-studied and computationally feasible statistical tools to explore the extremal dependence structure of high-dimensional data.

A novel link between classical principal component analysis and regular variation of random vectors opens up the opportunity to leverage knowledge from multivariate extreme value theory (Dr Kirstin Strokorb) and spectral approximation in kernel-based models (Dr Bertrand Gauthier). Professor Marco Marletta completes the local supervisory team through his expertise in spectral problems. In addition, Professor Dan Cooley (Colorado State University, College of Natural Sciences Professor Laureate) and Dr Christian Rohrbeck (University of Bath) will be advisors for this project and include questions of high priority to end users.

Project (2): Sparsity and structures in large-scale machine learning problems

This project will investigate, both from a theoretical and computational point of view, the design of novel model-based and data-driven feature extraction and sparsification strategies for the approximation of complex Machine Learning problems. Special attention will be drawn to kernel-based and artificial-neural-network-based methods, which are two of the most important families of modern Machine Learning algorithms.

The terminology “big data” is generally used to refer to datasets that are too large or complex for traditional data-processing technics to adequately deal with them. The exploration of such datasets with modern Machine Learning techniques therefore raises many theoretical and numerical challenges. The numerical complexity inherent to the processing of datasets indeed generally grows polynomially with their size, compromising de facto the analysis of very large datasets. In addition, the treatment of complex datasets often results in models involving a large number of parameters, making such models difficult to train while limiting their interpretability and increasing the risk of over/underfitting. Since such large-scale and complex datasets are more and more common in nowadays big-data and real-time-analytic era, their efficient processing is of great importance, not only at from purely scientific point of view, but also for many industrial and real-life applications.

In parallel with the use of high-performance computing solutions, many alternatives exist to try to overcome the difficulties inherent to the learning-with-big-data framework. Such operations need however to be applied with great care, since they generally have a significant impact on the quality of the final model, their effects being in addition often intrinsically connected; Existing theory surrounding such approximation schemes is generally quite modest. The goal of this project is the design and theoretical underpinning of novel approximation strategies for complex Machine Learning problems.

FURTHER DETAILS:

https://www.cardiff.ac.uk/study/postgraduate/funding/phd-studentships-and-projects
(Select “Cardiff School of Mathematics” as Department and either “Dr K Strokorb” or “Dr B Gauthier” as Supervisor.)