Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures

Matias Altamirano, Felipe Tobar
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:3204-3218, 2022.

Abstract

Kernel design for Multi-output Gaussian Processes (MOGP) has received increased attention recently, in particular, the Multi-Output Spectral Mixture kernel (MOSM) approach has been praised as a general model in the sense that it extends other approaches such as Linear Model of Corregionalization, Intrinsic Corregionalization Model and Cross-Spectral Mixture. MOSM relies on Cramer’s theorem to parametrise the power spectral densities (PSD) as a Gaussian mixture, thus, having a structural restriction: by assuming the existence of a PSD, the method is only suited for multi-output stationary processes. We develop a nonstationary extension of MOSM by proposing the family of harmonizable kernels for MOGPs, a class of kernels that contains both stationary and a vast majority of non-stationary processes. A main contribution of the proposed harmonizable kernels is that they automatically identify a possible nonstationary behaviour meaning that practitioners do not need to choose between stationary or non-stationary kernels. The proposed method is first validated on synthetic data with the purpose of illustrating the key properties of our approach, and then compared to existing MOGP methods on two real-world settings from finance and electroencephalography.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-altamirano22a, title = { Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures }, author = {Altamirano, Matias and Tobar, Felipe}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {3204--3218}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/altamirano22a/altamirano22a.pdf}, url = {https://proceedings.mlr.press/v151/altamirano22a.html}, abstract = { Kernel design for Multi-output Gaussian Processes (MOGP) has received increased attention recently, in particular, the Multi-Output Spectral Mixture kernel (MOSM) approach has been praised as a general model in the sense that it extends other approaches such as Linear Model of Corregionalization, Intrinsic Corregionalization Model and Cross-Spectral Mixture. MOSM relies on Cramer’s theorem to parametrise the power spectral densities (PSD) as a Gaussian mixture, thus, having a structural restriction: by assuming the existence of a PSD, the method is only suited for multi-output stationary processes. We develop a nonstationary extension of MOSM by proposing the family of harmonizable kernels for MOGPs, a class of kernels that contains both stationary and a vast majority of non-stationary processes. A main contribution of the proposed harmonizable kernels is that they automatically identify a possible nonstationary behaviour meaning that practitioners do not need to choose between stationary or non-stationary kernels. The proposed method is first validated on synthetic data with the purpose of illustrating the key properties of our approach, and then compared to existing MOGP methods on two real-world settings from finance and electroencephalography. } }
Endnote
%0 Conference Paper %T Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures %A Matias Altamirano %A Felipe Tobar %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-altamirano22a %I PMLR %P 3204--3218 %U https://proceedings.mlr.press/v151/altamirano22a.html %V 151 %X Kernel design for Multi-output Gaussian Processes (MOGP) has received increased attention recently, in particular, the Multi-Output Spectral Mixture kernel (MOSM) approach has been praised as a general model in the sense that it extends other approaches such as Linear Model of Corregionalization, Intrinsic Corregionalization Model and Cross-Spectral Mixture. MOSM relies on Cramer’s theorem to parametrise the power spectral densities (PSD) as a Gaussian mixture, thus, having a structural restriction: by assuming the existence of a PSD, the method is only suited for multi-output stationary processes. We develop a nonstationary extension of MOSM by proposing the family of harmonizable kernels for MOGPs, a class of kernels that contains both stationary and a vast majority of non-stationary processes. A main contribution of the proposed harmonizable kernels is that they automatically identify a possible nonstationary behaviour meaning that practitioners do not need to choose between stationary or non-stationary kernels. The proposed method is first validated on synthetic data with the purpose of illustrating the key properties of our approach, and then compared to existing MOGP methods on two real-world settings from finance and electroencephalography.
APA
Altamirano, M. & Tobar, F.. (2022). Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:3204-3218 Available from https://proceedings.mlr.press/v151/altamirano22a.html.

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