Laplace approximated Gaussian process state-space models

Jakob Lindinger, Barbara Rakitsch, Christoph Lippert
Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, PMLR 180:1199-1209, 2022.

Abstract

Gaussian process state-space models describe time series data in a probabilistic and non-parametric manner using a Gaussian process transition function. As inference is intractable, recent methods use variational inference and either rely on simplifying independence assumptions on the approximate posterior or learn the temporal states iteratively. The latter hampers optimization since the posterior over the presence can only be learned once the posterior governing the past has converged. We present a novel inference scheme that applies stochastic variational inference for the Gaussian process posterior and the Laplace approximation on the temporal states. This approach respects the conditional dependencies in the model and, through the Laplace approximation, treats the temporal states jointly, thereby avoiding their sequential learning. Our method is computationally efficient and leads to better calibrated predictions compared to state-of-the art alternatives on synthetic data and on a range of benchmark datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v180-lindinger22a, title = {Laplace approximated Gaussian process state-space models}, author = {Lindinger, Jakob and Rakitsch, Barbara and Lippert, Christoph}, booktitle = {Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence}, pages = {1199--1209}, year = {2022}, editor = {Cussens, James and Zhang, Kun}, volume = {180}, series = {Proceedings of Machine Learning Research}, month = {01--05 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v180/lindinger22a/lindinger22a.pdf}, url = {https://proceedings.mlr.press/v180/lindinger22a.html}, abstract = {Gaussian process state-space models describe time series data in a probabilistic and non-parametric manner using a Gaussian process transition function. As inference is intractable, recent methods use variational inference and either rely on simplifying independence assumptions on the approximate posterior or learn the temporal states iteratively. The latter hampers optimization since the posterior over the presence can only be learned once the posterior governing the past has converged. We present a novel inference scheme that applies stochastic variational inference for the Gaussian process posterior and the Laplace approximation on the temporal states. This approach respects the conditional dependencies in the model and, through the Laplace approximation, treats the temporal states jointly, thereby avoiding their sequential learning. Our method is computationally efficient and leads to better calibrated predictions compared to state-of-the art alternatives on synthetic data and on a range of benchmark datasets.} }
Endnote
%0 Conference Paper %T Laplace approximated Gaussian process state-space models %A Jakob Lindinger %A Barbara Rakitsch %A Christoph Lippert %B Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2022 %E James Cussens %E Kun Zhang %F pmlr-v180-lindinger22a %I PMLR %P 1199--1209 %U https://proceedings.mlr.press/v180/lindinger22a.html %V 180 %X Gaussian process state-space models describe time series data in a probabilistic and non-parametric manner using a Gaussian process transition function. As inference is intractable, recent methods use variational inference and either rely on simplifying independence assumptions on the approximate posterior or learn the temporal states iteratively. The latter hampers optimization since the posterior over the presence can only be learned once the posterior governing the past has converged. We present a novel inference scheme that applies stochastic variational inference for the Gaussian process posterior and the Laplace approximation on the temporal states. This approach respects the conditional dependencies in the model and, through the Laplace approximation, treats the temporal states jointly, thereby avoiding their sequential learning. Our method is computationally efficient and leads to better calibrated predictions compared to state-of-the art alternatives on synthetic data and on a range of benchmark datasets.
APA
Lindinger, J., Rakitsch, B. & Lippert, C.. (2022). Laplace approximated Gaussian process state-space models. Proceedings of the Thirty-Eighth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 180:1199-1209 Available from https://proceedings.mlr.press/v180/lindinger22a.html.

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