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。过去二十年间，GP因其卓越的预测能力（尤其在数据稀疏场景中）以及提供稳健不确定性估计的内在特性，已被引入机器学习领域。尽管如此，其性能高度依赖于核心方法的复杂定制，当部署标准设置和现成软件工具时，常导致实践者不满。GP最重要的构建模块当属核函数，它承担协方差算子的角色。绝大多数应用研究采用Matérn类平稳核；其结果往往是预测性能不佳且不确定性量化不切实际。非平稳核虽表现出改进的性能，但由于其函数形式更复杂，且需要大量努力与专业知识进行优化定义与调参，实际应用仍较少。本文旨在帮助机器学习实践者理解高斯过程中几种最常见的非平稳形式。我们通过代表性数据集展示多种核函数的实际效果，深入研究其特性，并系统比较其性能。基于研究发现，我们提出了一种新核函数，它融合了现有核函数中已识别的若干优势。