Periodic Kernel Approximation by Index Set Fourier Series Features

Anthony Tompkins, Fabio Ramos
Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, PMLR 115:486-496, 2020.

Abstract

Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for multi-dimensional problems such as in textures, crystallography, quantum mechanics, and robotics. Large datasets often make modelling periodicity untenable for otherwise powerful non-parametric methods like Gaussian Processes (GPs) which typically incur an $\mathcal{O}(N^3)$ computational cost, while approximate feature methods are impeded by their approximate accuracy. We introduce a method that efficiently decomposes multi-dimensional periodic kernels into a set of basis functions by exploiting multivariate Fourier series. Termed \emph{Index Set Fourier Series Features}, we show that our approximation produces significantly less predictive generalisation error than alternative approximations such as those based on random and deterministic Fourier features on regression problems with periodic data.

Cite this Paper

BibTeX
@InProceedings{pmlr-v115-tompkins20a, title = {Periodic Kernel Approximation by Index Set Fourier Series Features}, author = {Tompkins, Anthony and Ramos, Fabio}, booktitle = {Proceedings of The 35th Uncertainty in Artificial Intelligence Conference}, pages = {486--496}, year = {2020}, editor = {Adams, Ryan P. and Gogate, Vibhav}, volume = {115}, series = {Proceedings of Machine Learning Research}, month = {22--25 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v115/tompkins20a/tompkins20a.pdf}, url = {https://proceedings.mlr.press/v115/tompkins20a.html}, abstract = {Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for multi-dimensional problems such as in textures, crystallography, quantum mechanics, and robotics. Large datasets often make modelling periodicity untenable for otherwise powerful non-parametric methods like Gaussian Processes (GPs) which typically incur an $\mathcal{O}(N^3)$ computational cost, while approximate feature methods are impeded by their approximate accuracy. We introduce a method that efficiently decomposes multi-dimensional periodic kernels into a set of basis functions by exploiting multivariate Fourier series. Termed \emph{Index Set Fourier Series Features}, we show that our approximation produces significantly less predictive generalisation error than alternative approximations such as those based on random and deterministic Fourier features on regression problems with periodic data. } }
Endnote
%0 Conference Paper %T Periodic Kernel Approximation by Index Set Fourier Series Features %A Anthony Tompkins %A Fabio Ramos %B Proceedings of The 35th Uncertainty in Artificial Intelligence Conference %C Proceedings of Machine Learning Research %D 2020 %E Ryan P. Adams %E Vibhav Gogate %F pmlr-v115-tompkins20a %I PMLR %P 486--496 %U https://proceedings.mlr.press/v115/tompkins20a.html %V 115 %X Periodicity is often studied in timeseries modelling with autoregressive methods but is less popular in the kernel literature, particularly for multi-dimensional problems such as in textures, crystallography, quantum mechanics, and robotics. Large datasets often make modelling periodicity untenable for otherwise powerful non-parametric methods like Gaussian Processes (GPs) which typically incur an $\mathcal{O}(N^3)$ computational cost, while approximate feature methods are impeded by their approximate accuracy. We introduce a method that efficiently decomposes multi-dimensional periodic kernels into a set of basis functions by exploiting multivariate Fourier series. Termed \emph{Index Set Fourier Series Features}, we show that our approximation produces significantly less predictive generalisation error than alternative approximations such as those based on random and deterministic Fourier features on regression problems with periodic data.
APA
Tompkins, A. & Ramos, F.. (2020). Periodic Kernel Approximation by Index Set Fourier Series Features. Proceedings of The 35th Uncertainty in Artificial Intelligence Conference, in Proceedings of Machine Learning Research 115:486-496 Available from https://proceedings.mlr.press/v115/tompkins20a.html.

Related Material