Terry Lyons
From rough paths to streamed data
Abstract
Rough path theory is a mathematical framework for understanding streamed data and modelling its interactions; initiated in the early 1990s, has proved transformational to the mathematical description of physical systems and is still in rapid development. Simultaneously, and on a larger scale the data scientists have developed an impressive framework for analyzing scalar functions on data based on deep neural networks, with specialized and highly innovative sub-streams focused on images, and more recently on streamed data. They come from different directions, have different philosophies, but can learn from each other; both adopt a hierarchical approach to manage complexity. The precision of mathematics allows systematic analysis of problems with fewer features, which in turn allows understandable and effective prediction and classification with smaller datasets such as occur in health. The more detailed structure allows new objects such as a PDE based kernel, and better simulation techniques. We will survey some of the ideas that have emerged. We will also mention some problems that this mathematics and neural nets solve well together.
