Continuous-time Gaussian Process dynamics

Gaussian processes (GPs) are powerful tools to learn dynamics models that provide also uncertainty estimates for predictions. Most existing approaches are applied to one-step ahead predictions, which could be tempting from a mathematical and from an implementation perspective, since the GP can be directly conditioned on the data. However, one-step ahead predictions are typically not a good model for the continuous-time dynamics, and therefore they are not appropriate to be used as a vector field. Further it breaks, if the sensor measurements are taken at irregular-sampled step sizes, if sensor data are missing or if predictions are done at varying step sizes. Therefore, the aim of this thesis is to provide a GP model that can represent the original dynamics accurately and that can be trained via standard inference. These problems will addressed by the use of higher-order integrators along with GPs.