Scaled Vecchia Approximation for Fast Computer-Model Emulation
Scaled Vecchia Approximation for Fast Computer-Model Emulation
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DOI：
10.1137/20m1352156
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发表时间：
2020-05
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通讯作者：
M. Katzfuss;J. Guinness;E. Lawrence
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作者：
M. Katzfuss;J. Guinness;E. Lawrence
许多科学现象都是通过计算机实验来研究的，这些实验包括在改变输入设置的情况下多次运行计算机模型。高斯过程 (GP) 是一种流行的计算机实验分析工具，可以在输入设置之间进行插值，但直接 GP 推理对于大型数据集在计算上是不可行的。我们改编并扩展了空间统计中一类强大的 GP 方法，以实现大型计算机实验的可扩展分析和仿真。具体来说，我们在变换后的输入空间中应用 Vecchia 的有序条件近似，每个输入根据其与计算机模型响应的相关程度进行缩放。通过使用 Fisher 评分估计 GP 协方差函数中的参数，可以从数据中学习缩放比例。我们的方法具有高度可扩展性，能够在模型运行次数的近线性时间内进行估计、联合预测和模拟。在几个数值示例中，我们的方法大大优于现有方法。
Many scientific phenomena are studied using computer experiments consisting of multiple runs of a computer model while varying the input settings. Gaussian processes (GPs) are a popular tool for the analysis of computer experiments, enabling interpolation between input settings, but direct GP inference is computationally infeasible for large datasets. We adapt and extend a powerful class of GP methods from spatial statistics to enable the scalable analysis and emulation of large computer experiments. Specifically, we apply Vecchia's ordered conditional approximation in a transformed input space, with each input scaled according to how strongly it relates to the computer-model response. The scaling is learned from the data, by estimating parameters in the GP covariance function using Fisher scoring. Our methods are highly scalable, enabling estimation, joint prediction and simulation in near-linear time in the number of model runs. In several numerical examples, our approach substantially outperformed existing methods.