Learning and Inference in Structured, Higher Dimensional Stochastic Differential Systems

There are many areas of scientific research, business analysis and engineering for which stochastic differential equations are the natural form of system model. Fields such as environmental modelling, systems biology, ecological systems, weather, market dynamics, traffic networks, neural modelling and fMRI are all areas which have regularly used stochastic differential equations for describing system dynamics and making predictions. In these same areas, ever-increasing data quantities are becoming available, and there is a demand to utilise this data to refine and develop good system models. However it is very rare for this data to be directly used to develop stochastic differential models. Where stochastic differential equations are used, simulation methods still seem to be the standard modelling approach. Downloadable or purchasable tools for utilising inference and learning in these continuous-time and nonlinear systems are currently unavailable. The long-term aim of this research agenda is to develop, implement and promote tools for practical data-driven modelling for continuous-time stochastic systems. The focus is on inference and learning in high dimensional, nonlinear stochastic differential systems. We aim to make stochastic differential modelling as easy to do as simulation of stochastic differential equations (SDEs), fixed time modelling or deterministic methods. The immediate goal of this pump priming proposal was to coordinate, focus and develop existing independent early efforts in this direction at the three sites that form part of this proposal. We provided a coherent framework and test environment for the collaborative research. We researched, developed and firmly established a baseline set of methods for stochastic differential inference and learning. We proved the benefits and feasibility of these methods within the test environment, and provided clear demonstrations of the capabilities. This provided an initial toolset for stochastic modelling, and a firm grounding for establishing a larger scale European collaborative research agenda in this area.