The past does matter: correlation of subsequent states in trajectory predictions of Gaussian Process models

Steffen Ridderbusch, Sina Ober-Blöbaum, Paul Goulart
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:1752-1761, 2023.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-ridderbusch23a, title = {The past does matter: correlation of subsequent states in trajectory predictions of {G}aussian Process models}, author = {Ridderbusch, Steffen and Ober-Bl\"obaum, Sina and Goulart, Paul}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {1752--1761}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/ridderbusch23a/ridderbusch23a.pdf}, url = {https://proceedings.mlr.press/v216/ridderbusch23a.html}, 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.} }
Endnote
%0 Conference Paper %T The past does matter: correlation of subsequent states in trajectory predictions of Gaussian Process models %A Steffen Ridderbusch %A Sina Ober-Blöbaum %A Paul Goulart %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-ridderbusch23a %I PMLR %P 1752--1761 %U https://proceedings.mlr.press/v216/ridderbusch23a.html %V 216 %X 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.
APA
Ridderbusch, S., Ober-Blöbaum, S. & Goulart, P.. (2023). The past does matter: correlation of subsequent states in trajectory predictions of Gaussian Process models. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:1752-1761 Available from https://proceedings.mlr.press/v216/ridderbusch23a.html.

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