Approximate Uncertainty Propagation for Continuous Gaussian Process Dynamical Systems

Steffen Ridderbusch, Sina Ober-Blöbaum, Paul James Goulart

Keywords: Gaussian Processes, Dynamical Systems, Uncertainty Propagation

TL;DR: Using a local linearization based approach to approximating a Gaussian Process Dynamical System avoids an faulty independence assumption and enables us to deterministically solve for trajectories with uncertainty.

Abstract:

When learning continuous dynamical systems with Gaussian Processes, computing trajectories requires repeatedly mapping the distributions of uncertain states through the distribution of learned nonlinear functions, which is generally intractable. Since sampling-based approaches are computationally expensive, we consider approximations of the output and trajectory distributions.
We show that existing methods make an incorrect implicit independence assumption and underestimate the model-induced uncertainty. We propose a piecewise linear approximation of the GP model yielding a class of numerical solvers for efficient uncertainty estimates matching sampling-based methods.