Non-linear process convolutions for multi-output Gaussian processes

Mauricio A. Alvarez, Wil Ward, Cristian Guarnizo
Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, PMLR 89:1969-1977, 2019.

Abstract

The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of the approximated Gaussian process at the output of the Volterra series. The mean function and covariance function for the joint Gaussian process are derived using formulae for the product moments of Gaussian variables. We compare the performance of the non-linear model against the classical process convolution approach in one synthetic dataset and two real datasets.

Cite this Paper

BibTeX
@InProceedings{pmlr-v89-alvarez19a, title = {Non-linear process convolutions for multi-output Gaussian processes}, author = {Alvarez, Mauricio A. and Ward, Wil and Guarnizo, Cristian}, booktitle = {Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics}, pages = {1969--1977}, 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/alvarez19a/alvarez19a.pdf}, url = {https://proceedings.mlr.press/v89/alvarez19a.html}, abstract = {The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of the approximated Gaussian process at the output of the Volterra series. The mean function and covariance function for the joint Gaussian process are derived using formulae for the product moments of Gaussian variables. We compare the performance of the non-linear model against the classical process convolution approach in one synthetic dataset and two real datasets.} }
Endnote
%0 Conference Paper %T Non-linear process convolutions for multi-output Gaussian processes %A Mauricio A. Alvarez %A Wil Ward %A Cristian Guarnizo %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-alvarez19a %I PMLR %P 1969--1977 %U https://proceedings.mlr.press/v89/alvarez19a.html %V 89 %X The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of the approximated Gaussian process at the output of the Volterra series. The mean function and covariance function for the joint Gaussian process are derived using formulae for the product moments of Gaussian variables. We compare the performance of the non-linear model against the classical process convolution approach in one synthetic dataset and two real datasets.
APA
Alvarez, M.A., Ward, W. & Guarnizo, C.. (2019). Non-linear process convolutions for multi-output Gaussian processes. Proceedings of the Twenty-Second International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 89:1969-1977 Available from https://proceedings.mlr.press/v89/alvarez19a.html.

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