Cohort 4 of EPSRC CDT Industrially Focused Mathematical Modelling
Research Collabration with the Numerical Algorithm Group (NAG)
University of Oxford
Andrew Wiles Building
Radcliffe Observatory Quarter
My research is on analysis and implementations of randomised optimisation algorithms, and their applications to large-scale machine learning problems. Classical optimisation algorithms like the gradient descent and the trust-region method handle small to medium-sized inputs well. But they struggle to cope with increasingly large dataset presented by applications such as autonomous driving, face recognition and online recommender systems. Randomisation of those algorithms aims to simplify the dataset and/or the prediction model by sampling or projection so that they run faster with large dataset and complex models. In my research I aim to develop novel randomised versions of classical optimisation algorithms, provide rigorous probabilistic bounds on their errors and computational complexities, and provide high-performance implementations.
• Randomised Numerical Linear Algebra
• Sketching for linear and non-linear least squares (Reduce the dimensionality of the dataset for the optimisation computation)
• Sketching in the variable domain (Reduce the dimensionality of the feature space for the optimisation computation)
• High-performance implementation in C++
• Application to Machine Learning and Artificial Intelligence
2019 - 2020
• College Tutor, Part A Statistics
• Class Tutor, Part C Continuous Optimisation
• St Hughs College Tutor - A7 Numerical Analysis
• Departmental Matlab Demonstrator
• Teaching Assistant - MSc Continuous Optimisation
• Teaching Assistant - B6.3 Integer Programming
Prizes, awards, and scholarships:
• EPSRC CDT Scholarship (2017-2021)
Major / recent publications:
A Randomised Subspace Gauss-Newton Method for Nonlinear Least-Squares. Coralia Cartis (Oxford University); Jaroslav Fowkes (University of Oxford); Zhen Shao (University of Oxford), Thirty-seventh International Conference on Machine Learning, beyond first order methods in ML systems workshop, 2020.
Sparse sketching for sparse linear least squares. Zhen Shao (University of Oxford); Coralia Cartis (Oxford University); Jan Fiala (Numerical Algorithm Group Ltd.) Thirty-seventh International Conference on Machine Learning, beyond first order methods in ML systems workshop, 2020.