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Statistical Modelling vs. Machine Learning in Prediction of Extremes

PGR-P-727

Key facts

Type of research degree
PhD
Application deadline
Ongoing deadline
Country eligibility
International (open to all nationalities, including the UK)
Funding
Non-funded
Supervisors
Dr Leonid Bogachev and Professor Charles Taylor
Additional supervisors
Dr He Wang (Computing)
Schools
School of Computing, School of Mathematics
Research groups/institutes
Statistics
<h2 class="heading hide-accessible">Summary</h2>

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.

<h2 class="heading hide-accessible">Full description</h2>

<p>Statistical Modelling (SM) approach is based on choosing a &quot;suitable&quot; 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 &quot;typical&quot; 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 &quot;black&quot; box -&nbsp;we may be able to make a fairly good prediction but couldn&rsquo;t explain why it is such.</p> <p>There are ongoing discussions across these two communities on which of the approaches is preferable -&nbsp;with early ideas in favour of their &quot;convergence&quot; 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>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> <h5>References</h5> <p>[1] Breiman, L.Statistical modeling: the two cultures. <em>Statistical Science,</em> <strong>16</strong> (2001), 199&ndash;231, <a href="https://projecteuclid.org/download/pdf_1/euclid.ss/1009213726">https://projecteuclid.org/download/pdf_1/euclid.ss/1009213726</a><br /> [2] Gyarmati-Szab&oacute;, 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><br /> [3] 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><br /> [4] 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>&nbsp;(2013).</p> <p>The earliest start date for this project is 1 October 2020.</p>

<h2 class="heading">How to apply</h2>

<p>Formal applications for research degree study should be made online through the <a href="https://eps.leeds.ac.uk/maths-research-degrees/doc/apply">University website</a>. Please state clearly in the research information section&nbsp;that the research project you wish to be considered for is &lsquo;Statistical Modelling vs. Machine Learning in Prediction of Extremes&rsquo; as well as <a href="https://eps.leeds.ac.uk/maths/staff/4008/dr-leonid-bogachev">Dr Leonid Bogachev</a> as your proposed supervisor.</p> <p>If English is not your first language, you must provide evidence that you meet the University&#39;s minimum English language requirements (below).</p> <p><em>We welcome applications from all suitably-qualified candidates, but UK black and minority ethnic (BME) researchers are currently under-represented in our Postgraduate Research community, and we would therefore particularly encourage applications from UK BME candidates. All scholarships will be awarded on the basis of merit.</em></p>

<h2 class="heading heading--sm">Entry requirements</h2>

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.

<h2 class="heading heading--sm">English language requirements</h2>

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.

<h2 class="heading">Funding on offer</h2>

<p><strong>Self-funded students are also welcome to apply.</strong></p> <p><strong>UK&nbsp;students</strong>&nbsp;&ndash;&nbsp;The&nbsp;<a href="https://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarships-2021-january-deadline">Leeds Doctoral Scholarship (January deadline)</a>&nbsp;and the&nbsp;<a href="https://phd.leeds.ac.uk/funding/142-william-wright-smith-scholarship-2021">William Wright Smith Scholarship&nbsp;</a>are available to UK applicants. &nbsp;<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><strong>Non-UK students</strong>&nbsp;&ndash; The&nbsp;<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>&nbsp;is available to nationals of China. The&nbsp;<a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a>&nbsp;is available to support US citizens.&nbsp; <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds.</p>

<h2 class="heading">Contact details</h2>

<p>For further information please contact Doctoral College Admissions,<br /> e:&nbsp;<a href="mailto:maps.pgr.admissions@leeds.ac.uk">maps.pgr.admissions@leeds.ac.uk</a>, t: +44 (0)113 343 5057</p> <p>For furthe information regarding the project, please contact&nbsp;Dr Leonid Bogachev,<br /> e:&nbsp;<a href="mailto:L.V.Bogachev@leeds.ac.uk">L.V.Bogachev@leeds.ac.uk</a></p>


<h3 class="heading heading--sm">Linked research areas</h3>