Statistical Modelling vs. Machine Learning in Prediction of Extremes

The aim of this PhD project is to look at the interface between Statistical Modelling and Machine Learning to try and understand how to combine these approaches for uses in the extreme value domain, and potentially to achieve a better predictive power.

<p>Statistical Modelling (SM) approach is based on choosing a "suitable" model (e.g. linear regression, times series, etc.), fitting it to the data and then using it to predict the future. Machine Learning (ML) approach is based on searching algorithmically for "typical" patterns in the data (e.g. via Random Forests, Neural Networks, Deep Learning, etc.) and then using such patterns to predict the future. SM allows a better interpretation of results but the choice of a model may be subjective and disputable. On the other hand, ML methods often have a better prediction power but act as a "black" box – we may be able to make a fairly good prediction but couldn’t explain why it is such.</p> <p>There are ongoing discussions across these two communities on which of the approaches is preferable - with early ideas in favour of their "convergence" dating back to 1980s and advocated by some prominent statisticians such as Leo Breiman [1]. More recently, with the invention of Reinforced Learning [3,4], probabilistic concepts began to play a more significant part in ML algorithms, which are now focusing on predicting the distribution of a variable using iterated updates of the data (so-called training). This is reminiscent of the Bayesian approach in Statistics, and is worth exploring further. In this regard, analysis of extreme values raises interesting methodological questions. Extreme values are rare, but it is important and challenging to try and predict them due to potential high cost and undesirable impact. While there is a well-documented statistical theory for this purpose (see e.g. [2]), it is less clear if (and how) to use the ML technology there. The aim of this PhD project is to look at the interface of these two approaches to try and understand how to combine them and potentially achieve a better predictive power.</p> <p><strong>References</strong></p> <ol> <li>Breiman, L.Statistical modeling: the two cultures. <em>Statistical Science,</em> <strong>16</strong> (2001), 199–231, <a href="https://projecteuclid.org/download/pdf_1/euclid.ss/1009213726">https://projecteuclid.org/download/pdf_1/euclid.ss/1009213726</a></li> <li>Gyarmati-Szabó, J., Bogachev, L.V., and Chen, H. Nonstationary POT modelling of air pollution concentrations: Statistical analysis of the traffic and meteorological impact. <em>Environmetrics</em>, <strong>28 </strong>(2017), e2449; <a href="https://doi.org/10.1002/env.2449">doi:10.1002/env.2449</a></li> <li>Ha, D. and Schmidhuber, J. World models. <em>Zenodo</em> (online), 2018; <a href="https://doi.org/10.5281/zenodo.1207631">doi:10.5281/zenodo.1207631</a></li> <li>Kingma, D.P. and Welling, M. Auto-encoding variational Bayes. In: <em>Proceedings of the 2nd International Conference on Learning Representations (ICLR, 2014)</em>; <a href="https://arxiv.org/abs/1312.6114">arXiv:1312.6114</a> (2013).</li> </ol>

<p>Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University website</a>. Please state clearly in the Planned Course of Study that you are apply for <em><strong>PHD Statistics FT,</strong></em> in the research information section that the research project you wish to be considered for is <em><strong>Statistical Modelling vs. Machine Learning in Prediction of Extremes</strong></em> as well as <a href="https://eps.leeds.ac.uk/maths/staff/4008/dr-leonid-bogachev">Dr Leonid Bogachev</a> as your proposed supervisor and in the finance section, please state clearly <em><strong>the funding that you are applying for, if you are self-funding or externally sponsored</strong></em>.</p> <p>Successful candidates should have an excellent degree in mathematics, statistics, computing, or a closely allied discipline, with a strong background and research interests in one or more of the following areas: probability; random processes; statistics; data analytics; machine learning; artificial intelligence. Excellent computer coding skills in R and/or Python are desirable</p> <p>You will work under the joint supervision by the Department of Statistics and the School of Computing, and with the involvement of the Leeds Institute for Data Analytics (LIDA).</p> <p>If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below).</p> <p style="margin-bottom:11px"><em>As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability.</em></p> <p class="MsoNoSpacing">Applications will be considered after the closing date.  Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed.</p> <p class="MsoNoSpacing"><strong>Please note that you must provide the following documents in support of your application by the closing date of Monday 6 January 2025 if applying for the China Scholarship Council-University of Leeds Scholarship, Monday 3 February 2025 if applying for Leeds Doctoral Scholarship or Tuesday 1 April 2025 for Leeds Opportunity Research Scholarship.</strong></p> <p><strong>If you are applying for the School of Mathematics Scholarship 2025/26, or with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application:</strong></p> <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in mathematics, statistics, computing, or a closely allied discipline, with a strong background and research interests in one or more of the following areas: probability; random processes; statistics; data analytics; machine learning; artificial intelligence. Excellent computer coding skills in R and/or Python are desirable.

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.0 overall with at least 5.5 in each component (reading, writing, listening and speaking) or equivalent. The test must be dated within two years of the start date of the course in order to be valid.

<p style="margin-bottom:12px"><strong>Self-Funded or externally sponsored students are welcome to apply.</strong></p> <p><strong>UK</strong> – The <a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarship-2025-faculty-of-engineering-and-physical-sciences#:~:text=Key%20facts&text=One%20Leeds%20Doctoral%20Scholarship%20is,rata%20for%20part%2Dtime%20study.">Leeds Doctoral Scholarship</a> <strong>(closing date: Monday 3 February 2025)</strong>, <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> <strong>(closing date: Tuesday 1 April 2025)</strong> and <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to UK applicants.</p> <p><strong>Non-UK</strong> – <a href="https://phd.leeds.ac.uk/funding/55-school-of-mathematics-scholarship-2025-26">School of Mathematics Scholarship 2025/26</a> <strong>(open from October 2024)</strong> are available to all International applicants.  The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> <strong>(closing date: Monday 6 January 2025)</strong> is available to nationals of China. The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p> <p>You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award.</p> <p><strong>Important:</strong> Please note that that the award does <em><strong>not</strong></em> cover the costs associated with moving to the UK.  All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. </p> <p>Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.</p>

<p>For further information about your application, please contact PGR Admissions by email to <a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a></p> <p>For further information about this project, please contact Dr Leonid Bogachev by email to <a href="mailto:L.V.Bogachev@leeds.ac.uk">L.V.Bogachev@leeds.ac.uk</a></p>