The Mathematics of Complex Streamed Data
Abstract
Multimodal streamed data is essentially different to unimodal streamed data. Consider this: 'A commuter arrives at a bus stop before the bus' – they catch it; 'The bus arrives first' – they miss it. These are the same two events, but the order changes everything. Yet most models treat these as identical: 'A bus and a person arrived' They ignore timing and relationships. This simplification isn't harmless. A timed series gives no information about order within sampling intervals. As a result, the sampling rate has to come from the bottom up if it is to preserve this order information. Rough path theory makes a radical change and describes the stream over an interval using a group element. According to the choice of group it is possible to capture order information and to allow a top down description of the data stream without using essential information about the order of events. This approach to describing streamed data is important to data science because it reduces the dimension needed for descriptive feature sets and so reduces the size of the data set needed to train. There are numerous prize winning illustrations of the methodology in use and the impact can be measured in the hundreds of millions of US dollars.
Watch recording ↗About the speaker
Terry Lyons FLSW FRSE FRS is the Wallis Professor Emeritus and Professor of Mathematics at the University of Oxford, a fellow of St Anne's College, Oxford and a Faculty Fellow at The Alan Turing Institute. He is currently PI of the DataSıg and of the complementary research programme CIMDA-Oxford. He was the President of the London Mathematical Society (2013-2015), the Director (2011-2015) of the Oxford Man Institute of Quantitative Finance and the Director of the Wales Institute of Mathematical and Computational Sciences (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 – particularly to Finance and more generally to the summarising of large complex data. More specifically, his interests are in developing mathematical tools that 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. He is, in particular, recognised for developing what is now known as the theory of rough paths.