The Past Does Matter: Correlation of Subsequent States in Trajectory Predictions of Gaussian Process Models
This work addresses a computational challenge in Gaussian Process models for dynamical systems, though it appears incremental as it builds on and corrects prior methods.
The paper identified that previous uncertainty propagation methods for Gaussian Process dynamical models incorrectly assumed independence between subsequent states in trajectory predictions, and proposed a novel piecewise linear approximation to address this issue, demonstrating its implications through continuous ordinary differential equation models.
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.