Interpolation error of Gaussian process regression for misspecified case

Alexey Zaytsev, Evgenya Romanenkova, Dmitry Ermilov
Proceedings of the Seventh Workshop on Conformal and Probabilistic Prediction and Applications, PMLR 91:83-95, 2018.

Abstract

An interpolation error is an integral of the squared error of a regression model over a domain of interest. We consider the interpolation error for the case of misspecified Gaussian process regression: a used covariance function differs from a true one. We derive the interpolation error for a grid design of experiments for an arbitrary covariance function. Then we consider particular types of covariance functions from theoretical and practical points of view. For $\textitMatern_1/2$ covariance function poor estimation of parameters only slightly affects the quality of interpolation. For the most common covariance functions including $\textitMatern_3/2$ and squared exponential covariance functions poor choose of parameters of covariance functions leads to a bad quality of interpolation.

Cite this Paper

BibTeX
@InProceedings{pmlr-v91-zaytsev18a, title = {Interpolation error of {G}aussian process regression for misspecified case}, author = {Zaytsev, Alexey and Romanenkova, Evgenya and Ermilov, Dmitry}, booktitle = {Proceedings of the Seventh Workshop on Conformal and Probabilistic Prediction and Applications}, pages = {83--95}, year = {2018}, editor = {Gammerman, Alex and Vovk, Vladimir and Luo, Zhiyuan and Smirnov, Evgueni and Peeters, Ralf}, volume = {91}, series = {Proceedings of Machine Learning Research}, month = {11--13 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v91/zaytsev18a/zaytsev18a.pdf}, url = {https://proceedings.mlr.press/v91/zaytsev18a.html}, abstract = {An interpolation error is an integral of the squared error of a regression model over a domain of interest. We consider the interpolation error for the case of misspecified Gaussian process regression: a used covariance function differs from a true one. We derive the interpolation error for a grid design of experiments for an arbitrary covariance function. Then we consider particular types of covariance functions from theoretical and practical points of view. For $\textitMatern_1/2$ covariance function poor estimation of parameters only slightly affects the quality of interpolation. For the most common covariance functions including $\textitMatern_3/2$ and squared exponential covariance functions poor choose of parameters of covariance functions leads to a bad quality of interpolation.} }
Endnote
%0 Conference Paper %T Interpolation error of Gaussian process regression for misspecified case %A Alexey Zaytsev %A Evgenya Romanenkova %A Dmitry Ermilov %B Proceedings of the Seventh Workshop on Conformal and Probabilistic Prediction and Applications %C Proceedings of Machine Learning Research %D 2018 %E Alex Gammerman %E Vladimir Vovk %E Zhiyuan Luo %E Evgueni Smirnov %E Ralf Peeters %F pmlr-v91-zaytsev18a %I PMLR %P 83--95 %U https://proceedings.mlr.press/v91/zaytsev18a.html %V 91 %X An interpolation error is an integral of the squared error of a regression model over a domain of interest. We consider the interpolation error for the case of misspecified Gaussian process regression: a used covariance function differs from a true one. We derive the interpolation error for a grid design of experiments for an arbitrary covariance function. Then we consider particular types of covariance functions from theoretical and practical points of view. For $\textitMatern_1/2$ covariance function poor estimation of parameters only slightly affects the quality of interpolation. For the most common covariance functions including $\textitMatern_3/2$ and squared exponential covariance functions poor choose of parameters of covariance functions leads to a bad quality of interpolation.
APA
Zaytsev, A., Romanenkova, E. & Ermilov, D.. (2018). Interpolation error of Gaussian process regression for misspecified case. Proceedings of the Seventh Workshop on Conformal and Probabilistic Prediction and Applications, in Proceedings of Machine Learning Research 91:83-95 Available from https://proceedings.mlr.press/v91/zaytsev18a.html.

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