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Topological methods in machine learning and statistics

Applications are invited for our EPSRC funded Doctoral Training Partnership (DTP) PhD studentship for the project “Topological methods in machine learning and statistics” starting 1 April 2022. Successful applicants will receive an annual stipend (bursary) of £17,609, including inner London weighting, plus payment of their full-time tuition fees for a period of 36-months (3 years).

Applicants must be classified as a home (UK) tuition fee paying student to be eligible for this studentship.

The Project

This research project is centred around Topological Data Analysis (TDA) which amounts to leveraging topological information for machine learning and statistical inference. TDA has proved to be useful for such tasks as graph classification, community detection, goodness of fit tests etc, which are fundamental questions in computational chemistry, neuroscience, material science, biology and other areas of science and technology. You will focus on analysing theoretical properties as well as empirical performance of some TDA methods in machine learning and statistics, in particular:

  • prove limit theorems (law of large numbers, central limit theorems) for topological features and provide non-asymptotic error bounds;
  • design statistical tests based on topological features;
  • analyse and design machine learning algorithms where topological features are implemented.

Please contact Dr Xiaochuan Yang at xiaochuan.yang@brunel.ac.uk to arrange an informal discussion about the project.


Skills and Experience

This project would suit a strong candidate with a background in Probability, Statistics, and/or Topology. It would be advantageous to have experience or interest in Computer Science (Algorithms). Applicants should be motivated to work on fundamental problems in the field, and have a strong sense of curiosity. You should be highly motivated, able to work independently as well as in a team, collaborate with others and communicate effectively.

Academic Entry Criteria

You will have or be expected to receive a 1st class or 2:1 honours degree in Mathematics. A postgraduate masters degree is not required but may be an advantage.


How to apply

Please submit the documents below as a single PDF file by email to cedps-pgr-office@brunel.ac.uk by 14:00 on Monday 28 February 2022.

  • Your up-to-date CV;
  • Your personal statement (300 to 500 words) summarising your background, skills and experience. Please state the name of the project supervisor at the top of your personal statement;
  • Your Undergraduate/Postgraduate Masters degree certificate(s) and transcript(s);
  • Your English Language qualification of IELTS 6.5 overall (minimum 6.0 in all sections) or equivalent, if applicable;
  • Contact details for TWO referees, one of whom can be a member of Brunel University academic staff.

Meet the Supervisor(s)

Xiaochuan Yang - I am Lecturer in Mathematics/Statistics at Brunel. My research interest lies in Probability Theory and its connection with analysis, statistics, and other disciplines of science and technology such as physics, machine learning, geometric and topological data analysis. Before joining Brunel, I held the position of EPSRC postdoc at the University of Bath, the Luxembourg-Singapore bilateral postdoc position, and visiting assistant professor position at Michigan State University.