Scalable Gaussian Process Separation for Kernels with a Non-Stationary Phase

Jan Graßhoff, Alexandra Jankowski, Philipp Rostalski
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:3722-3731, 2020.

Abstract

The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel matrix. Previous methods, however, cannot easily deal with mixtures of non-stationary processes. This paper investigates an efficient GP framework, that extends structured kernel interpolation methods to GPs with a non-stationary phase. We particularly treat the separation of nonstationary sources, which is a problem that commonly arises e.g. in spatio-temporal biomedical datasets. Our approach employs multiple sets of non-equidistant inducing points to account for the non-stationarity and retrieve Toeplitz and Kronecker structure in the kernel matrix allowing for efficient inference and kernel learning. Our approach is demonstrated on numerical examples and large spatio-temporal biomedical problems.

Cite this Paper

BibTeX
@InProceedings{pmlr-v119-grasshoff20a, title = {Scalable {G}aussian Process Separation for Kernels with a Non-Stationary Phase}, author = {Gra{\ss}hoff, Jan and Jankowski, Alexandra and Rostalski, Philipp}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {3722--3731}, year = {2020}, editor = {III, Hal Daumé and Singh, Aarti}, volume = {119}, series = {Proceedings of Machine Learning Research}, month = {13--18 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v119/grasshoff20a/grasshoff20a.pdf}, url = {https://proceedings.mlr.press/v119/grasshoff20a.html}, abstract = {The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel matrix. Previous methods, however, cannot easily deal with mixtures of non-stationary processes. This paper investigates an efficient GP framework, that extends structured kernel interpolation methods to GPs with a non-stationary phase. We particularly treat the separation of nonstationary sources, which is a problem that commonly arises e.g. in spatio-temporal biomedical datasets. Our approach employs multiple sets of non-equidistant inducing points to account for the non-stationarity and retrieve Toeplitz and Kronecker structure in the kernel matrix allowing for efficient inference and kernel learning. Our approach is demonstrated on numerical examples and large spatio-temporal biomedical problems.} }
Endnote
%0 Conference Paper %T Scalable Gaussian Process Separation for Kernels with a Non-Stationary Phase %A Jan Graßhoff %A Alexandra Jankowski %A Philipp Rostalski %B Proceedings of the 37th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2020 %E Hal Daumé III %E Aarti Singh %F pmlr-v119-grasshoff20a %I PMLR %P 3722--3731 %U https://proceedings.mlr.press/v119/grasshoff20a.html %V 119 %X The application of Gaussian processes (GPs) to large data sets is limited due to heavy memory and computational requirements. A variety of methods has been proposed to enable scalability, one of which is to exploit structure in the kernel matrix. Previous methods, however, cannot easily deal with mixtures of non-stationary processes. This paper investigates an efficient GP framework, that extends structured kernel interpolation methods to GPs with a non-stationary phase. We particularly treat the separation of nonstationary sources, which is a problem that commonly arises e.g. in spatio-temporal biomedical datasets. Our approach employs multiple sets of non-equidistant inducing points to account for the non-stationarity and retrieve Toeplitz and Kronecker structure in the kernel matrix allowing for efficient inference and kernel learning. Our approach is demonstrated on numerical examples and large spatio-temporal biomedical problems.
APA
Graßhoff, J., Jankowski, A. & Rostalski, P.. (2020). Scalable Gaussian Process Separation for Kernels with a Non-Stationary Phase. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:3722-3731 Available from https://proceedings.mlr.press/v119/grasshoff20a.html.

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