Gaussian processes (GPs) are flexible, probabilistic, nonparametric models widely used in fields such as spatial statistics and machine learning. A drawback of Gaussian processes is their computational cost, with $O(N^3)$ time and $O(N^2)$ memory complexity, which makes them prohibitive for large data sets. Numerous approximation techniques have been proposed to address this limitation. In this work, we systematically compare the accuracy of different Gaussian process approximations with respect to likelihood evaluation, parameter estimation, and prediction, explicitly accounting for the computational time required. We analyze the trade-off between accuracy and runtime on multiple simulated and large-scale real-world data sets and find that Vecchia approximations consistently provide the best accuracy-runtime trade-off across most settings considered.

翻译：高斯过程（GPs）是一种灵活的概率非参数模型，广泛应用于空间统计学和机器学习等领域。高斯过程的一个缺点是其计算成本较高，具有 $O(N^3)$ 的时间复杂度和 $O(N^2)$ 的内存复杂度，这使得它们难以应用于大规模数据集。为克服这一限制，已提出了多种近似技术。本研究系统比较了不同高斯过程近似方法在似然评估、参数估计和预测方面的精度，并明确考虑了所需的计算时间。我们在多个模拟和大规模真实数据集上分析了精度与运行时间之间的权衡关系，发现 Vecchia 近似方法在大多数考虑的场景中始终提供最佳的精度-运行时间权衡。