A General Framework for Vecchia Approximations of Gaussian Processes
A General Framework for Vecchia Approximations of Gaussian Processes
复制标题
DOI：
10.1214/19-sts755
复制
发表时间：
2021-02-01
影响因子：
5.7
通讯作者：
Guinness, Joseph
中科院分区：
文献类型：
--
作者：
Katzfuss, Matthias;Guinness, Joseph
高斯过程（GP）通常用作函数，时间序列和空间场的模型，但它们在大型数据集上是不可行的。专注于建模数据的典型设置为GP加上加性噪声项，我们提出了Vecchia（J. Roy.中央集权主义者Soc. Ser B 50（1988）297-312）方法作为GP近似的框架。我们表明，我们的一般Vecchia方法包含许多流行的现有GP近似的特殊情况下，允许在一个统一的框架内的不同方法之间的比较。通过有向无环图表示模型，我们确定了推理所需的矩阵的稀疏性，这导致了关于计算特性的新见解。基于这些结果，我们提出了一种新的稀疏一般Vecchia近似，它确保了大型空间数据集的计算可行性，但可以导致相当大的改进近似精度超过Vecchia的原始方法。我们提供了几个理论结果，并进行数值比较。最后，我们的指导方针使用韦基亚近似空间统计。
Gaussian processes (GPs) are commonly used as models for functions, time series, and spatial fields, but they are computationally infeasible for large datasets. Focusing on the typical setting of modeling data as a GP plus an additive noise term, we propose a generalization of the Vecchia (J. Roy. Statist. Soc. Ser B 50 (1988) 297-312) approach as a framework for GP approximations. We show that our general Vecchia approach contains many popular existing GP approximations as special cases, allowing for comparisons among the different methods within a unified framework. Representing the models by directed acyclic graphs, we determine the sparsity of the matrices necessary for inference, which leads to new insights regarding the computational properties. Based on these results, we propose a novel sparse general Vecchia approximation, which ensures computational feasibility for large spatial datasets but can lead to considerable improvements in approximation accuracy over Vecchia's original approach. We provide several theoretical results and conduct numerical comparisons. We conclude with guidelines for the use of Vecchia approximations in spatial statistics.