Analytic Long-Term Forecasting with Periodic Gaussian Processes

Nooshin HajiGhassemi, Marc Deisenroth
Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, PMLR 33:303-311, 2014.

Abstract

Gaussian processes are a state-of-the-art method for learning models from data. Data with an underlying periodic structure appears in many areas, e.g., in climatology or robotics. It is often important to predict the long-term evolution of such a time series, and to take the inherent periodicity explicitly into account. In a Gaussian process, periodicity can be accounted for by an appropriate kernel choice. However, the standard periodic kernel does not allow for analytic long-term forecasting, which requires to map distributions through the Gaussian process. To address this shortcoming, we re-parametrize the periodic kernel, which, in combination with a double approximation, allows for analytic long-term forecasting of a periodic state evolution with Gaussian processes. Our model allows for probabilistic long-term forecasting of periodic processes, which can be valuable in Bayesian decision making, optimal control, reinforcement learning, and robotics.

Cite this Paper

BibTeX
@InProceedings{pmlr-v33-hajighassemi14, title = {{Analytic Long-Term Forecasting with Periodic Gaussian Processes}}, author = {HajiGhassemi, Nooshin and Deisenroth, Marc}, booktitle = {Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics}, pages = {303--311}, year = {2014}, editor = {Kaski, Samuel and Corander, Jukka}, volume = {33}, series = {Proceedings of Machine Learning Research}, address = {Reykjavik, Iceland}, month = {22--25 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v33/hajighassemi14.pdf}, url = {https://proceedings.mlr.press/v33/hajighassemi14.html}, abstract = {Gaussian processes are a state-of-the-art method for learning models from data. Data with an underlying periodic structure appears in many areas, e.g., in climatology or robotics. It is often important to predict the long-term evolution of such a time series, and to take the inherent periodicity explicitly into account. In a Gaussian process, periodicity can be accounted for by an appropriate kernel choice. However, the standard periodic kernel does not allow for analytic long-term forecasting, which requires to map distributions through the Gaussian process. To address this shortcoming, we re-parametrize the periodic kernel, which, in combination with a double approximation, allows for analytic long-term forecasting of a periodic state evolution with Gaussian processes. Our model allows for probabilistic long-term forecasting of periodic processes, which can be valuable in Bayesian decision making, optimal control, reinforcement learning, and robotics.} }
Endnote
%0 Conference Paper %T Analytic Long-Term Forecasting with Periodic Gaussian Processes %A Nooshin HajiGhassemi %A Marc Deisenroth %B Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2014 %E Samuel Kaski %E Jukka Corander %F pmlr-v33-hajighassemi14 %I PMLR %P 303--311 %U https://proceedings.mlr.press/v33/hajighassemi14.html %V 33 %X Gaussian processes are a state-of-the-art method for learning models from data. Data with an underlying periodic structure appears in many areas, e.g., in climatology or robotics. It is often important to predict the long-term evolution of such a time series, and to take the inherent periodicity explicitly into account. In a Gaussian process, periodicity can be accounted for by an appropriate kernel choice. However, the standard periodic kernel does not allow for analytic long-term forecasting, which requires to map distributions through the Gaussian process. To address this shortcoming, we re-parametrize the periodic kernel, which, in combination with a double approximation, allows for analytic long-term forecasting of a periodic state evolution with Gaussian processes. Our model allows for probabilistic long-term forecasting of periodic processes, which can be valuable in Bayesian decision making, optimal control, reinforcement learning, and robotics.
RIS
TY - CPAPER TI - Analytic Long-Term Forecasting with Periodic Gaussian Processes AU - Nooshin HajiGhassemi AU - Marc Deisenroth BT - Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics DA - 2014/04/02 ED - Samuel Kaski ED - Jukka Corander ID - pmlr-v33-hajighassemi14 PB - PMLR DP - Proceedings of Machine Learning Research VL - 33 SP - 303 EP - 311 L1 - http://proceedings.mlr.press/v33/hajighassemi14.pdf UR - https://proceedings.mlr.press/v33/hajighassemi14.html AB - Gaussian processes are a state-of-the-art method for learning models from data. Data with an underlying periodic structure appears in many areas, e.g., in climatology or robotics. It is often important to predict the long-term evolution of such a time series, and to take the inherent periodicity explicitly into account. In a Gaussian process, periodicity can be accounted for by an appropriate kernel choice. However, the standard periodic kernel does not allow for analytic long-term forecasting, which requires to map distributions through the Gaussian process. To address this shortcoming, we re-parametrize the periodic kernel, which, in combination with a double approximation, allows for analytic long-term forecasting of a periodic state evolution with Gaussian processes. Our model allows for probabilistic long-term forecasting of periodic processes, which can be valuable in Bayesian decision making, optimal control, reinforcement learning, and robotics. ER -
APA
HajiGhassemi, N. & Deisenroth, M.. (2014). Analytic Long-Term Forecasting with Periodic Gaussian Processes. Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 33:303-311 Available from https://proceedings.mlr.press/v33/hajighassemi14.html.

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