Sparse Gaussian Processes with Spherical Harmonic Features

Vincent Dutordoir, Nicolas Durrande, James Hensman
Proceedings of the 37th International Conference on Machine Learning, PMLR 119:2793-2802, 2020.

Abstract

We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations. Our inference scheme is comparable to variational Fourier features, but it does not suffer from the curse of dimensionality, and leads to diagonal covariance matrices between inducing variables. This enables a speed-up in inference, because it bypasses the need to invert large covariance matrices. Our experiments show that our model is able to fit a regression model for a dataset with 6 million entries two orders of magnitude faster compared to standard sparse GPs, while retaining state of the art accuracy. We also demonstrate competitive performance on classification with non-conjugate likelihoods.

Cite this Paper


BibTeX
@InProceedings{pmlr-v119-dutordoir20a, title = {Sparse {G}aussian Processes with Spherical Harmonic Features}, author = {Dutordoir, Vincent and Durrande, Nicolas and Hensman, James}, booktitle = {Proceedings of the 37th International Conference on Machine Learning}, pages = {2793--2802}, 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/dutordoir20a/dutordoir20a.pdf}, url = {http://proceedings.mlr.press/v119/dutordoir20a.html}, abstract = {We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations. Our inference scheme is comparable to variational Fourier features, but it does not suffer from the curse of dimensionality, and leads to diagonal covariance matrices between inducing variables. This enables a speed-up in inference, because it bypasses the need to invert large covariance matrices. Our experiments show that our model is able to fit a regression model for a dataset with 6 million entries two orders of magnitude faster compared to standard sparse GPs, while retaining state of the art accuracy. We also demonstrate competitive performance on classification with non-conjugate likelihoods.} }
Endnote
%0 Conference Paper %T Sparse Gaussian Processes with Spherical Harmonic Features %A Vincent Dutordoir %A Nicolas Durrande %A James Hensman %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-dutordoir20a %I PMLR %P 2793--2802 %U http://proceedings.mlr.press/v119/dutordoir20a.html %V 119 %X We introduce a new class of inter-domain variational Gaussian processes (GP) where data is mapped onto the unit hypersphere in order to use spherical harmonic representations. Our inference scheme is comparable to variational Fourier features, but it does not suffer from the curse of dimensionality, and leads to diagonal covariance matrices between inducing variables. This enables a speed-up in inference, because it bypasses the need to invert large covariance matrices. Our experiments show that our model is able to fit a regression model for a dataset with 6 million entries two orders of magnitude faster compared to standard sparse GPs, while retaining state of the art accuracy. We also demonstrate competitive performance on classification with non-conjugate likelihoods.
APA
Dutordoir, V., Durrande, N. & Hensman, J.. (2020). Sparse Gaussian Processes with Spherical Harmonic Features. Proceedings of the 37th International Conference on Machine Learning, in Proceedings of Machine Learning Research 119:2793-2802 Available from http://proceedings.mlr.press/v119/dutordoir20a.html.

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