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.

翻译：高斯过程（GP）是一种流行的统计技术，用于从数据中进行随机函数逼近和不确定性量化。在过去二十年中，GP因其卓越的预测能力（尤其是在数据稀疏场景下）以及其固有的提供稳健不确定性估计的能力而被纳入机器学习领域。尽管如此，其性能高度依赖于核心方法论的复杂定制，当部署标准设置和现成软件工具时，这往往会导致实践者的不满。可以说，GP最重要的构建模块是核函数，它扮演着协方差算子的角色。绝大多数应用研究中使用Matern类的平稳核函数；这常常导致预测性能低下和不切实际的不确定性量化。非平稳核函数显示出改进的性能，但由于其更复杂的函数形式以及定义和优化它们所需的相关努力和专业知识，很少被使用。在此视角中，我们希望帮助机器学习实践者理解高斯过程的一些最常见的非平稳性形式。我们通过代表性数据集展示了多种核函数的实际应用，仔细研究了它们的性质，并比较了它们的性能。基于我们的发现，我们提出了一种新核函数，它结合了现有核函数的一些确定优势。