Gaussian processes (GPs) are sophisticated distributions to model functional data. Whilst theoretically appealing, they are computationally cumbersome except for small datasets. We implement two methods for scaling GP inference in Stan: First, a general sparse approximation using a directed acyclic dependency graph. Second, a fast, exact method for regularly spaced data modeled by GPs with stationary kernels using the fast Fourier transform. Based on benchmark experiments, we offer guidance for practitioners to decide between different methods and parameterizations. We consider two real-world examples to illustrate the package. The implementation follows Stan's design and exposes performant inference through a familiar interface. Full posterior inference for ten thousand data points is feasible on a laptop in less than 20 seconds.

翻译：高斯过程（GPs）是用于建模函数数据的复杂分布。尽管在理论上具有吸引力，但除了小型数据集外，它们具有计算上的难点。我们使用有向无环依赖图实现了两种方法以在Stan中扩展GP推断：首先是用于一般稀疏近似的方法，其次是使用快速傅里叶变换针对使用平稳核的GPs模型的定期间隔数据的快速准确方法。基于基准实验，我们为从业人员提供了在不同方法和参数化之间进行选择的指导。我们考虑了两个现实世界的例子来说明该程序包。该实现遵循Stan的设计并通过熟悉的界面公开可行的推断。在笔记本电脑上，对于一万个数据点的全后验推断在不到20秒内就可以实现。