Daniel graduated from Lancaster University in 2016 with an MSc in Data Science, having completed a BSc in Mathematics at the University of Reading in 2015. During the Summer of 2016, he worked on a collaborative project with Admiral Group PLC, implementing regression models and other supervised learning techniques to predict consumer call response rates. After working for a few years in transport simulation development and logistics, he decided to return to academia to combine interesting areas of Graph Theory and High Dimensional Regression Modelling for a PhD. He usually spends his free time going on long walks, following cricket and listening to a mixture of progressive and jazz fusion music, as well as playing the odd card game now and then.

Research project title:
Multivariate Regression on High-Dimensional Networks

Supervisor(s):
Sandipan Roy, Vangelis Evangelou

Project description:
A crucial feature of many modern data sets is their inherent graphical (network) structure embedded in them. Gaussian Graphical Models, known by various other names, are commonly used in Statistics to encode a graphical conditional relationship onto a multivariate Gaussian distribution. Many scientific applications manifest a high dimensionality combined with a sparse graph structure, which can hinder inference and high-level interpretation when fitting graphical models onto relevant data. However, as exemplified through geospatial crime data, the implementation of a regression-based transformation through a penalty term in the log-likelihood function can efficiently and informatively infer a covariate relationship between a high number of connected nodes (crime rates for different regions) with a smaller number of secondary variables (socioeconomic factors). Daniel’s project aims to establish tractability conditions for parameter estimation under a generalised expression of this new Gaussian graphical model, through an iterative algorithmic procedure. Where a graph structure is not known, a Lasso-like penalty must be employed in tandem with the regression penalty. Further considerations include the extension of the single graph case to that of an evolving graph, mainly in a temporal sense.