Structured Variational Inference in Partially Observable Unstable Gaussian Process State Space Models

Sebastian Curi, Silvan Melchior, Felix Berkenkamp, Andreas Krause
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:147-157, 2020.

Abstract

We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic contribution is a novel approximate posterior that can be calculated efficiently using a single forward and backward pass along the training trajectories. The forward-backward pass is inspired on Kalman smoothing for linear dynamical systems but generalizes to GPSSMs. Our second contribution is a modification of the conditioning step that effectively lowers the Kalman gain. This modification is crucial to attaining good test performance where no measurements are available. Finally, we show experimentally that our learning algorithm performs well in stable and unstable real systems with hidden states.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-curi20a, title = {Structured Variational Inference in Partially Observable UnstableGaussian Process State Space Models}, author = {Curi, Sebastian and Melchior, Silvan and Berkenkamp, Felix and Krause, Andreas}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {147--157}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/curi20a/curi20a.pdf}, url = {https://proceedings.mlr.press/v120/curi20a.html}, abstract = {We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic contribution is a novel approximate posterior that can be calculated efficiently using a single forward and backward pass along the training trajectories. The forward-backward pass is inspired on Kalman smoothing for linear dynamical systems but generalizes to GPSSMs. Our second contribution is a modification of the conditioning step that effectively lowers the Kalman gain. This modification is crucial to attaining good test performance where no measurements are available. Finally, we show experimentally that our learning algorithm performs well in stable and unstable real systems with hidden states.} }
Endnote
%0 Conference Paper %T Structured Variational Inference in Partially Observable Unstable Gaussian Process State Space Models %A Sebastian Curi %A Silvan Melchior %A Felix Berkenkamp %A Andreas Krause %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-curi20a %I PMLR %P 147--157 %U https://proceedings.mlr.press/v120/curi20a.html %V 120 %X We propose a new variational inference algorithm for learning in Gaussian Process State-Space Models (GPSSMs). Our algorithm enables learning of unstable and partially observable systems, where previous algorithms fail. Our main algorithmic contribution is a novel approximate posterior that can be calculated efficiently using a single forward and backward pass along the training trajectories. The forward-backward pass is inspired on Kalman smoothing for linear dynamical systems but generalizes to GPSSMs. Our second contribution is a modification of the conditioning step that effectively lowers the Kalman gain. This modification is crucial to attaining good test performance where no measurements are available. Finally, we show experimentally that our learning algorithm performs well in stable and unstable real systems with hidden states.
APA
Curi, S., Melchior, S., Berkenkamp, F. & Krause, A.. (2020). Structured Variational Inference in Partially Observable Unstable Gaussian Process State Space Models. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:147-157 Available from https://proceedings.mlr.press/v120/curi20a.html.

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