论文标题
通过可和谐的光谱混合物进行非平稳的多输出高斯工艺
Nonstationary multi-output Gaussian processes via harmonizable spectral mixtures
论文作者
论文摘要
多输出高斯流程（MOGP）的内核设计最近受到了越来越多的关注。特别是，多输出光谱混合物内核（MOSM）ARXIV：1709.01298方法已被称赞为一种通用模型，因为它扩展了其他方法，例如诸如跨内在的跨环化模型和跨光谱混合物的线性模型。 MOSM依靠Cramér定理将功率谱密度（PSD）作为高斯混合物参数，因此具有结构性限制：通过假设存在PSD，该方法仅适用于多出输出固定式施用。我们通过提出MOGP的可和谐内核家族来开发MOSM的非平稳扩展，Mogps是一类包含固定和绝大多数非平稳过程的内核。所提出的可协调内核的主要贡献是，它们会自动确定可能的非组织行为，这意味着从业者不需要在固定或非平稳的内核之间进行选择。首先在综合数据上验证了所提出的方法，目的是说明我们方法的关键特性，然后与金融和脑电图的两个现实世界中的现有MOGP方法进行了比较。
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 Cramér'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.
