Gaussian Process Kernels for Pattern Discovery and Extrapolation

Andrew Wilson, Ryan Adams
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(3):1067-1075, 2013.

Abstract

Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral density – the Fourier transform of a kernel – with a Gaussian mixture. The proposed kernels support a broad class of stationary covariances, but Gaussian process inference remains simple and analytic. We demonstrate the proposed kernels by discovering patterns and performing long range extrapolation on synthetic examples, as well as atmospheric CO2 trends and airline passenger data. We also show that it is possible to reconstruct several popular standard covariances within our framework.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-wilson13, title = {Gaussian Process Kernels for Pattern Discovery and Extrapolation}, author = {Wilson, Andrew and Adams, Ryan}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {1067--1075}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {3}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/wilson13.pdf}, url = {https://proceedings.mlr.press/v28/wilson13.html}, abstract = {Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral density – the Fourier transform of a kernel – with a Gaussian mixture. The proposed kernels support a broad class of stationary covariances, but Gaussian process inference remains simple and analytic. We demonstrate the proposed kernels by discovering patterns and performing long range extrapolation on synthetic examples, as well as atmospheric CO2 trends and airline passenger data. We also show that it is possible to reconstruct several popular standard covariances within our framework.} }
Endnote
%0 Conference Paper %T Gaussian Process Kernels for Pattern Discovery and Extrapolation %A Andrew Wilson %A Ryan Adams %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-wilson13 %I PMLR %P 1067--1075 %U https://proceedings.mlr.press/v28/wilson13.html %V 28 %N 3 %X Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral density – the Fourier transform of a kernel – with a Gaussian mixture. The proposed kernels support a broad class of stationary covariances, but Gaussian process inference remains simple and analytic. We demonstrate the proposed kernels by discovering patterns and performing long range extrapolation on synthetic examples, as well as atmospheric CO2 trends and airline passenger data. We also show that it is possible to reconstruct several popular standard covariances within our framework.
RIS
TY - CPAPER TI - Gaussian Process Kernels for Pattern Discovery and Extrapolation AU - Andrew Wilson AU - Ryan Adams BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/26 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-wilson13 PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 3 SP - 1067 EP - 1075 L1 - http://proceedings.mlr.press/v28/wilson13.pdf UR - https://proceedings.mlr.press/v28/wilson13.html AB - Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral density – the Fourier transform of a kernel – with a Gaussian mixture. The proposed kernels support a broad class of stationary covariances, but Gaussian process inference remains simple and analytic. We demonstrate the proposed kernels by discovering patterns and performing long range extrapolation on synthetic examples, as well as atmospheric CO2 trends and airline passenger data. We also show that it is possible to reconstruct several popular standard covariances within our framework. ER -
APA
Wilson, A. & Adams, R.. (2013). Gaussian Process Kernels for Pattern Discovery and Extrapolation. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(3):1067-1075 Available from https://proceedings.mlr.press/v28/wilson13.html.

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