Ward, W.O.C., Ryder, T., Prangle, D. et al. (1 more author) (Submitted: 2019) Variational bridge constructs for grey box modelling with Gaussian processes. arXiv. (Submitted)
Abstract
Latent force models are systems whereby there is a mechanistic model describing the dynamics of the system state, with some unknown forcing term that is approximated with a Gaussian process. If such dynamics are non-linear, it can be difficult to estimate the posterior state and forcing term jointly, particularly when there are system parameters that also need estimating. This paper uses black-box variational inference to jointly estimate the posterior, designing a multivariate extension to local inverse autoregressive flows as a flexible approximater of the system. We compare estimates on systems where the posterior is known, demonstrating the effectiveness of the approximation, and apply to problems with non-linear dynamics, multi-output systems and models with non-Gaussian likelihoods.
Metadata
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Copyright, Publisher and Additional Information: | © 2019 The Author(s). For reuse permissions, please contact the Author(s). | ||||
Dates: |
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Institution: | The University of Sheffield | ||||
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Computer Science (Sheffield) | ||||
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Depositing User: | Symplectic Sheffield | ||||
Date Deposited: | 02 Nov 2020 13:43 | ||||
Last Modified: | 02 Nov 2020 13:45 | ||||
Published Version: | https://arxiv.org/abs/1906.09199 | ||||
Status: | Submitted |