Black-Box Inference for Non-Linear Latent Force Models

Wil Ward, Tom Ryder, Dennis Prangle, Mauricio Alvarez
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:3088-3098, 2020.

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 approximator 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v108-ward20a, title = {Black-Box Inference for Non-Linear Latent Force Models}, author = {Ward, Wil and Ryder, Tom and Prangle, Dennis and Alvarez, Mauricio}, booktitle = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics}, pages = {3088--3098}, year = {2020}, editor = {Chiappa, Silvia and Calandra, Roberto}, volume = {108}, series = {Proceedings of Machine Learning Research}, month = {26--28 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v108/ward20a/ward20a.pdf}, url = {https://proceedings.mlr.press/v108/ward20a.html}, 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 approximator 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.} }
Endnote
%0 Conference Paper %T Black-Box Inference for Non-Linear Latent Force Models %A Wil Ward %A Tom Ryder %A Dennis Prangle %A Mauricio Alvarez %B Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2020 %E Silvia Chiappa %E Roberto Calandra %F pmlr-v108-ward20a %I PMLR %P 3088--3098 %U https://proceedings.mlr.press/v108/ward20a.html %V 108 %X 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 approximator 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.
APA
Ward, W., Ryder, T., Prangle, D. & Alvarez, M.. (2020). Black-Box Inference for Non-Linear Latent Force Models. Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 108:3088-3098 Available from https://proceedings.mlr.press/v108/ward20a.html.

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