Professor Terry Lyons

Professor Terry Lyons is the Wallis Professor Emeritus and Professor of Mathematics at the University of Oxford and visiting Professor at Imperial College London. He is currently PI of the DataSıg program (primarily funded by EPSRC), and of the complementary research programme CIMDA-Oxford. He was a founding member (2007) of, and then Director (2011-2015) of, the Oxford Man Institute of Quantitative Finance; he was the Director of the Wales Institute of Mathematical and Computational Sciences (WIMCS; 2008-2011). He came to Oxford in 2000 having previously been Professor of Mathematics at Imperial College London (1993-2000), and before that he held the Colin Maclaurin Chair at Edinburgh (1985-93).

Professor Lyons’s long-term research interests are all focused on Rough Paths, Stochastic Analysis, and applications to the use of data science with streamed data particularly to finance, healthcare, human computer interfaces and more generally to the summarising of large complex data. More specifically, his interests are in developing mathematical tools such as neural rough differential equations and software tools like RoughPy that deal with mathematical operations like shuffle product and logarithm for elements of the tensor algebra. These tools, and rough analysis more generally, can be used to effectively model and describe high dimensional systems that exhibit randomness as well as the complex multimodal data streams that arise in human activity. Professor Lyons is involved in a wide range of problems from pure mathematical ones to questions of efficient numerical calculation. DataSıg is a project that bridges from the fundamental mathematics to application contexts where novel techniques for analysing streamed data have potential to contribute value; these contexts include mental health, action recognition, astronomy, cybersecurity, … The CIMDA-Oxford research partnership aims to address a broader range of mathematical and engineering challenges arising from multi-dimensional big data.

Talk Title

Rough Analysis and Anomalous Streams

Talk Summary

Multi modal streams of information arise naturally in many engineering contexts. Rough path theory is an area of mathematics that fuses the control theory of Sussmann, Brockett and Fleiss with the analysis of Young to form a calculus that can efficiently describe the interaction and evolution of complex oscillatory systems.

One mathematical tool coming from this theory is the signature of a stream. Using software packages like RoughPy one can reduce an interval of streamed data to a relatively parsimonious vector representation known as the signature that is independent of the intensity of sampling in the stream. RoughPy provides tools for working with streams. The signature feature has many significant mathematics properties and has emerged as a suitable starting point in a range of practical challenges, leading to a number of prize winning and innovative outcomes.

One challenge in streamed data is to start with a corpus of ‘normal’ streamed data and recognise that a new stream is not plausibly from the same family defined by the corpus. One advantage of the theoretical perspectives is that one can design methods, such as this outlier detection methodology that respects natural invariants of streamed data. For example, outlier scores should produce the same outcomes if

1. the corpus and the data are rescaled (e.g. from Fahrenheit to centigrade)
2. a channel is duplicated or not
3. the streams are pre or post pended by common meta data.

A signature based method that achieves all these invariants has shown value in several real world applications.

A networking lunch will be provided at the end of the seminar.