Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures

TL;DR

This paper introduces a nonstationary extension of Multi-Output Spectral Mixture kernels for Gaussian processes, enabling automatic identification of nonstationary behaviors and broadening applicability to real-world nonstationary data.

Contribution

It proposes harmonizable kernels for MOGPs that encompass both stationary and non-stationary processes, removing the need for manual kernel selection.

Findings

Successfully models nonstationary data in synthetic experiments.

Outperforms existing MOGP methods on finance and EEG datasets.

Automatically detects nonstationary behavior without prior specification.

Abstract

Kernel design for Multi-output Gaussian Processes (MOGP) has received increased attention recently. In particular, the Multi-Output Spectral Mixture kernel (MOSM) arXiv:1709.01298 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 Cram\'er'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 applications. 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.