Multioutput Convolution Spectral Mixture for Gaussian Processes

Multioutput Gaussian processes (MOGPs) are an extension of Gaussian processes (GPs) for predicting multiple output variables (also called channels/tasks) simultaneously. In this article, 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 multioutput convolution spectral mixture (MOCSM) kernel. The results of extensive experiments on synthetic and real-life data sets 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 multioutput SM 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.