The Past Does Matter: Correlation of Subsequent States in Trajectory Predictions of Gaussian Process Models

Steffen Ridderbusch, Sina Ober-Blöbaum, Paul James Goulart

Keywords: Gaussian Processes, Uncertainty Propagation, Dynamical Systems

TL;DR: Predicting trajectories with uncertainty is challenging and we show an approximate way to do it while including correlation with past states.

Abstract: Computing the distribution of trajectories from a Gaussian Process model of a dynamical system is an important challenge in utilizing such models. Motivated by the computational cost of sampling-based approaches, we consider approximations of the model's output and trajectory distribution. We show that previous work on uncertainty propagation, focussed on discrete state-space models, incorrectly included an independence assumption between subsequent states of the predicted trajectories. Expanding these ideas to continuous ordinary differential equation models, we illustrate the implications of this assumption and propose a novel piecewise linear approximation of Gaussian Processes to mitigate them.