Low rank approximations of matrices with a focus on statistical applications
This proposal will investigate the structured low-rank approximation (SLRA) problem.
Broadly speaking, this work will involve a synergy of statistics, linear algebra and optimisation, and has relevance to problems in other disciplines. The problem will be shown to have implications for the analysis of time series, but is an interesting optimisation problem in its own right which requires a linear algebraic approach.
Traditionally linear algebra has seen applications in a wide variety of problems in multivariate statistics but the last decade has generated a number of new settings in which such techniques are being applied in statistics. This proposal also sees statistical and probabilistic techniques being applied back to linear algebra to obtain exciting breakthroughs. The student will have much training in working across disciplinary boundaries.
We are interested in pursuing this project and welcome applications if you are self-funded or have funding from other sources, including government sponsorships or your employer.
Please contact the supervisor when you want to pursue this project, citing the project title in your email, or find out more about our PhD programme in Mathematics.