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.

翻译：多输出高斯进程(MOGP)的内核设计最近受到越来越多的关注,特别是多输出光谱混凝土内核内核(MOSM):1709.01298(MOSM)方法被称赞为通用模型,因为它推广了其他方法,如Cor区域化线形模型、Intrinsic Corcionalization 模型和交叉分界混集体。MOSM依靠Cram\er的理论将能量光谱密度(PSD)作为高斯混合体,因此具有结构性限制:假设存在私营部门司,该方法仅适合多输出固定应用。我们开发了MOSMSM的非静止扩展,为此提出了MOGPs可协调的内核单元,该类内核包括固定和绝大多数非静止过程。拟议的内核内核部分的主要贡献是,它们自动确定一种可能真实的、非静止的方法,与当时的合成方法相比,意味着我们目前不需选择的固定的系统或合成方法。