Vecchia Approximations of Gaussian-Process Predictions
Vecchia Approximations of Gaussian-Process Predictions
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DOI：
10.1007/s13253-020-00401-7
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发表时间：
2020-06-23
影响因子：
1.4
通讯作者：
Zilber, Daniel
中科院分区：
文献类型：
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作者：
Katzfuss, Matthias;Guinness, Joseph;Zilber, Daniel
高斯过程（GP）是用于地理空间分析、非参数回归和机器学习的高度灵活的函数估计器，但它们在计算上对于大型数据集是不可行的。Vecchia近似的GP已被用来使参数推断的可能性的快速评估。在这里，我们研究在观察到的和未观察到的位置的空间预测的Vecchia近似，包括获得联合预测分布在大的位置集。我们考虑一个通用的Vecchia框架GP预测，其中包含一些新的和一些现有的特殊情况。我们从理论上和数值上研究了这些方法的精度和计算特性，证明了我们的新方法在空间位置的总数中表现出线性计算复杂性。我们表明，框架内的某些选择可以有很大的影响不确定性量化和计算成本，从而导致具体的建议，哪些方法是最适合于各种设置。我们还将我们的方法应用于叶绿素荧光的卫星数据集，表明新方法比现有方法更快或更准确，并减少了预测图中不切实际的伪影。本文件所附补充材料可上网查阅。
Gaussian processes (GPs) are highly flexible function estimators used for geospatial analysis, nonparametric regression, and machine learning, but they are computationally infeasible for large datasets. Vecchia approximations of GPs have been used to enable fast evaluation of the likelihood for parameter inference. Here, we study Vecchia approximations of spatial predictions at observed and unobserved locations, including obtaining joint predictive distributions at large sets of locations. We consider a general Vecchia framework for GP predictions, which contains some novel and some existing special cases. We study the accuracy and computational properties of these approaches theoretically and numerically, proving that our new methods exhibit linear computational complexity in the total number of spatial locations. We show that certain choices within the framework can have a strong effect on uncertainty quantification and computational cost, which leads to specific recommendations on which methods are most suitable for various settings. We also apply our methods to a satellite dataset of chlorophyll fluorescence, showing that the new methods are faster or more accurate than existing methods and reduce unrealistic artifacts in prediction maps. Supplementary materials accompanying this paper appear on-line.