Multi-Output Convolution Spectral Mixture for Gaussian Processes

Multi-output Gaussian processes (MOGPs) are recently extended by using spectral mixture kernel, which enables expressively pattern extrapolation with a strong interpretation. In particular, Multi-Output Spectral Mixture kernel (MOSM) is a recent, powerful state of the art method. However, MOSM cannot reduce to the ordinary spectral mixture kernel (SM) when using a single channel. Moreover, when the spectral density of different channels is either very close or very far from each other in the frequency domain, MOSM generates unreasonable scale effects on cross weights which produces an incorrect description of the channel correlation structure. In this paper, we tackle these drawbacks and introduce a principled multi-output convolution spectral mixture kernel (MOCSM) framework. In our framework, we model channel dependencies through convolution of time and phase delayed spectral mixtures between different channels.