Multi-Output Convolution Spectral Mixture for Gaussian Processes
This work addresses the need for improved multi-output prediction in Gaussian processes, offering a novel kernel that avoids undesirable scale effects seen in prior methods, though it is incremental in advancing kernel design for this domain.
The paper tackles the problem of predicting multiple output variables simultaneously in multi-output Gaussian processes by designing a new kernel called Multi-Output Convolution Spectral Mixture (MOCSM) that models cross-channel dependencies through convolution in the spectral domain, achieving state-of-the-art performance in experiments on synthetic and real-life datasets.
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.