Multi-Output Convolution Spectral Mixture for Gaussian Processes

TL;DR

This paper introduces the Multi-Output Convolution Spectral Mixture (MOCSM) kernel for Gaussian Processes, enabling improved modeling of multiple outputs by capturing cross-channel dependencies through spectral domain convolution, with demonstrated state-of-the-art performance.

Contribution

The paper proposes a novel MOCSM kernel for multi-output Gaussian processes that models cross-channel dependencies via spectral convolution, outperforming existing kernels.

Findings

MOCSM kernel achieves state-of-the-art results on synthetic and real datasets.

It reduces to the Spectral Mixture kernel in single-channel cases.

Compared to Multi-Output Spectral Mixture kernel, MOCSM avoids undesirable scale effects.

Abstract

Multi-output Gaussian processes (MOGPs) are an extension of Gaussian Processes (GPs) for predicting multiple output variables (also called channels, tasks) simultaneously. In this paper we use the convolution theorem to design a new kernel for MOGPs, by modeling cross channel dependencies through cross convolution of time and phase delayed components in the spectral domain. The resulting kernel is called Multi-Output Convolution Spectral Mixture (MOCSM) kernel. Results of extensive experiments on synthetic and real-life datasets demonstrate the advantages of the proposed kernel and its state of the art performance. MOCSM enjoys the desirable property to reduce to the well known Spectral Mixture (SM) kernel when a single-channel is considered. A comparison with the recently introduced Multi-Output Spectral Mixture kernel reveals that this is not the case for the latter kernel, which contains quadratic terms that generate undesirable scale effects when the spectral densities of different channels are either very close or very far from each other in the frequency domain.