Sequential Inference for Latent Force Models

Jouni Hartikainen, Simo Sarkka
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:349-356, 2011.

Abstract

Latent force models (LFMs) are hybrid models combining mechanistic principles with non-parametric components. In this article, we shall show how LFMs can be equivalently formulated and solved using the state variable approach. We shall also show how the Gaussian process prior used in LFMs can be equivalently formulated as a linear statespace model driven by a white noise process and how inference on the resulting model can be efficiently implemented using Kalman filter and smoother. Then we shall show how the recently proposed switching LFM can be reformulated using the state variable approach, and how we can construct a probabilistic model for the switches by formulating a similar switching LFM as a switching linear dynamic system (SLDS). We illustrate the performance of the proposed methodology in simulated scenarios and apply it to inferring the switching points in GPS data collected from car movement data in urban environment.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-hartikainen11a, title = {Sequential Inference for Latent Force Models}, author = {Hartikainen, Jouni and Sarkka, Simo}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {349--356}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/hartikainen11a/hartikainen11a.pdf}, url = {https://proceedings.mlr.press/r9/hartikainen11a.html}, abstract = {Latent force models (LFMs) are hybrid models combining mechanistic principles with non-parametric components. In this article, we shall show how LFMs can be equivalently formulated and solved using the state variable approach. We shall also show how the Gaussian process prior used in LFMs can be equivalently formulated as a linear statespace model driven by a white noise process and how inference on the resulting model can be efficiently implemented using Kalman filter and smoother. Then we shall show how the recently proposed switching LFM can be reformulated using the state variable approach, and how we can construct a probabilistic model for the switches by formulating a similar switching LFM as a switching linear dynamic system (SLDS). We illustrate the performance of the proposed methodology in simulated scenarios and apply it to inferring the switching points in GPS data collected from car movement data in urban environment.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Sequential Inference for Latent Force Models %A Jouni Hartikainen %A Simo Sarkka %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-hartikainen11a %I PMLR %P 349--356 %U https://proceedings.mlr.press/r9/hartikainen11a.html %V R9 %X Latent force models (LFMs) are hybrid models combining mechanistic principles with non-parametric components. In this article, we shall show how LFMs can be equivalently formulated and solved using the state variable approach. We shall also show how the Gaussian process prior used in LFMs can be equivalently formulated as a linear statespace model driven by a white noise process and how inference on the resulting model can be efficiently implemented using Kalman filter and smoother. Then we shall show how the recently proposed switching LFM can be reformulated using the state variable approach, and how we can construct a probabilistic model for the switches by formulating a similar switching LFM as a switching linear dynamic system (SLDS). We illustrate the performance of the proposed methodology in simulated scenarios and apply it to inferring the switching points in GPS data collected from car movement data in urban environment. %Z Reissued by PMLR on 04 October 2026.
APA
Hartikainen, J. & Sarkka, S.. (2011). Sequential Inference for Latent Force Models. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:349-356 Available from https://proceedings.mlr.press/r9/hartikainen11a.html. Reissued by PMLR on 04 October 2026.

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