Outline

This project aims at investigating, 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 (e.g., parallelisation, computation using GPUs), many alternatives exist to try to overcome the difficulties inherent to the learning-with-big-data framework. For instance, problems related to the size of the datasets might be addressed through sample-size and dimension reduction techniques, while feature extraction, low-rank approximation and sparsity-inducing techniques might be used to prevent the model complexity to explode. 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; to make the matter worse, existing theory surrounding such approximation schemes is generally quite modest. The goal of this project is thus the design of novel approximation strategies for complex Machine Learning problems, and the study of their theoretical underpinning.

The School of Mathematics of Cardiff University provides an excellent research environment for postgraduate students. Bespoke training for the project will be provided by the supervisory team, and the student will also have the opportunity to attend a selection of relevant training courses. The School colloquia and seminars and the student-led SIAM-IMA Chapter offer great opportunities for exchanges on cutting-edge research.

The student will acquire strong theoretical and practical skills in Mathematics, Data Analysis and Machine Learning. These sets of skills are highly sought after on the current job market, opening doors to many academic and industrial careers, both in applied and theoretical directions. Machine learning being by essence an interdisciplinary discipline, the student will strengthen their expertise in Mathematics through the study of the relevant underlying mathematical concepts (e.g., reproducing kernel Hilbert spaces, operator theory, optimisation, multiresolution analysis, statistics) and will in parallel develop strong computational/numerical abilities through the implementation and the benchmarking of the proposed methodologies.

The student will have the opportunity to attend bespoke training relevant to the project and to their personal development, and will follow a selection of advanced courses proposed by the School of Mathematics national collaborative network (MAGIC, NATCOR and APTS) and by Cardiff’s Doctoral Academy. All in all, this project opens up outstanding career prospects, both from an academic and industrial point of view.

What is funded

The 3.5 year studentship includes UK/EU fees, stipend (amount for 2020/21 is £15285) and a research training grant to cover costs such as research consumables, training, conferences and travel.

Eligibility

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 6.0 in each skills component. Further acceptable qualifications can be found at View Website

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

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.

Shortlisted candidates will be invited to attend an interview in April.