Computational challenges in data science typically involve high-dimensional problems. Although huge data sets are available, their size is often limited relative to the problem dimension, and breakthroughs are typically based on recognising some underlying structure in the data that enable the problem to be solved in an inherently lower-dimensional space. We will discuss several examples of dimensionality-reduction through detection of underlying structure and discuss them both from the point of view of theoretical analysis and through empirical results.

Raphael Hauser studied Mathematics and Theoretical Physics at ETH Zurich and then joined the School of Operations Research and Industrial Engineering at Cornel University (USA), where he gained a PhD in Operations Research. After postdoctoral research at the Department of Applied Mathematics in Cambridge (UK), he joined the faculty of the Computer Science Department at the University of Oxford (UK) and is now an Associate Professor in Numerical Mathematics at the Oxford Mathematical Institute, Tanaka Fellow of Applied Mathematics at Pembroke College Oxford,  and a Turing Fellow at the Alan Turing Institute in London (UK). His research interests lie in numerical optimisation, convex analysis, applied probability and data science.