Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple resolutions to achieve fast inference and that can (approximately) represent any spatial covariance structure. We consider two special cases of this multi-resolution-approximation framework, a taper version and a domain-partitioning (block) version. We describe theoretical properties and inference procedures, and study the computational complexity of the methods. Numerical comparisons and an application to satellite data are also provided.

中文翻译：

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高斯过程预测的 Vecchia 近似

高斯过程是用于空间、时间和功能数据的流行且灵活的模型，但它们在计算上对于大型数据集是不可行的。我们讨论高斯过程近似，它在多个分辨率下使用基函数来实现快速推理，并且可以（近似）表示任何空间协方差结构。我们考虑这种多分辨率近似框架的两种特殊情况，锥形版本和域分区（块）版本。我们描述了理论特性和推理过程，并研究了这些方法的计算复杂性。还提供了数值比较和卫星数据的应用。