Harmonizable mixture kernels with variational Fourier features

Zheyang Shen, Markus Heinonen, Samuel Kaski
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:3273-3282, 2019.

Abstract

The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatment of non-stationary kernels, HMK supports harmonizable covariances, a wide subset of kernels including all stationary and many non-stationary covariances. We also propose variational Fourier features, an inter-domain sparse GP inference framework that offers a representative set of ’inducing frequencies’. We show that harmonizable mixture kernels interpolate between local patterns, and that variational Fourier features offers a robust kernel learning framework for the new kernel family.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-shen19c, title = {Harmonizable mixture kernels with variational Fourier features}, author = {Shen, Zheyang and Heinonen, Markus and Kaski, Samuel}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {3273--3282}, year = {2019}, editor = {Chaudhuri, Kamalika and Sugiyama, Masashi}, volume = {89}, series = {Proceedings of Machine Learning Research}, month = {16--18 Apr}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v89/shen19c/shen19c.pdf}, url = {https://proceedings.mlr.press/v89/shen19c.html}, abstract = {The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatment of non-stationary kernels, HMK supports harmonizable covariances, a wide subset of kernels including all stationary and many non-stationary covariances. We also propose variational Fourier features, an inter-domain sparse GP inference framework that offers a representative set of ’inducing frequencies’. We show that harmonizable mixture kernels interpolate between local patterns, and that variational Fourier features offers a robust kernel learning framework for the new kernel family.} }
Endnote
%0 Conference Paper %T Harmonizable mixture kernels with variational Fourier features %A Zheyang Shen %A Markus Heinonen %A Samuel Kaski %B Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Masashi Sugiyama %F pmlr-v89-shen19c %I PMLR %P 3273--3282 %U https://proceedings.mlr.press/v89/shen19c.html %V 89 %X The expressive power of Gaussian processes depends heavily on the choice of kernel. In this work we propose the novel harmonizable mixture kernel (HMK), a family of expressive, interpretable, non-stationary kernels derived from mixture models on the generalized spectral representation. As a theoretically sound treatment of non-stationary kernels, HMK supports harmonizable covariances, a wide subset of kernels including all stationary and many non-stationary covariances. We also propose variational Fourier features, an inter-domain sparse GP inference framework that offers a representative set of ’inducing frequencies’. We show that harmonizable mixture kernels interpolate between local patterns, and that variational Fourier features offers a robust kernel learning framework for the new kernel family.
APA
Shen, Z., Heinonen, M. & Kaski, S.. (2019). Harmonizable mixture kernels with variational Fourier features. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:3273-3282 Available from https://proceedings.mlr.press/v89/shen19c.html.

Related Material