Extracting Non-Homogeneous Dependency Structures: Where Optimisation meets Statistics



Alex Gibberd


Lecturer in Statistics - Lancaster University

Abstract: Rapid advancement in measurement systems and sensor networks means we can now investigate complex systems with increasingly fine detail. In science, we usually gather data with the aim of increasing our understanding of a system. For example, we may want to know which regions of the brain communicate throughout an epilepsy seizure, or how different computers behaviour is linked throughout a cyber-attack.

This talk will discuss recent tools that myself and others are developing for the quantification of dependency in complex dynamic processes. That is, we attempt not only to model dependency between components of a system, but also how these vary over time. The models and algorithms developed during this work take a very holistic approach to describing system behaviour. Harnessing the power of modern computing, we develop algorithms that can automatically find important components within very large statistical models. Rather than modelling a system in a bottom-up manner, i.e. from it’s constituent components independently, we focus on modelling the system jointly, as a whole. For example, instead of modelling individual stock prices, we may wish (and now can) model a whole collection of stocks together. Furthermore, I will demonstrate how we may find key points in time/space where dependency structure across a system appears to change very abruptly. Such points often coincide with complex qualitative changes in a systems behaviour, for instance, we give an example where changes in gene dependency pathways of a fruit fly align with its life-cycle development.

Exploratory methods, such as those presented here provide a useful link between descriptive, data-driven, and hypothesis driven scientific study. I will conclude the talk by discussing how the inter-disciplinary research can operates in practice, and why I believe the combination of statistics and optimisation can help us answer some of the most pressing scientific questions.

Bio: I am a Lecturer in Statistics at Lancaster University. Prior to this, I was a Postdoctoral Research Associate at Imperial College London, and completed my PhD at University College London in 2017. My research interests can broadly be described under the heading of multivariate time-series analysis. More specifically, I am interested in so-called high-dimensional statistical models applied to time-series analysis, in this case the number of model parameters can grow faster than data size. I work to develop new optimisation algorithms that can search for both graphical dependency and changepoint structures in such models.