The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their superior prediction abilities, especially in data-sparse scenarios, and their inherent ability to provide robust uncertainty estimates. Even so, their performance highly depends on intricate customizations of the core methodology, which often leads to dissatisfaction among practitioners when standard setups and off-the-shelf software tools are being deployed. Arguably the most important building block of a GP is the kernel function which assumes the role of a covariance operator. Stationary kernels of the Mat\'ern class are used in the vast majority of applied studies; poor prediction performance and unrealistic uncertainty quantification are often the consequences. Non-stationary kernels show improved performance but are rarely used due to their more complicated functional form and the associated effort and expertise needed to define and tune them optimally. In this perspective, we want to help ML practitioners make sense of some of the most common forms of non-stationarity for Gaussian processes. We show a variety of kernels in action using representative datasets, carefully study their properties, and compare their performances. Based on our findings, we propose a new kernel that combines some of the identified advantages of existing kernels.

高斯过程常用于数据的随机函数逼近和不确定性量化，在机器学习中它们表现出优秀的预测能力，尤其在数据稀缺场景下，但核函数作为高斯过程的重要构建模块，通常需要进行复杂的定制，我们通过研究代表性数据集中多种核函数的表现、性质和性能，提出了一种融合现有核函数优点的新核函数。

深入的高斯过程的非稳态卷积核的统一视角