用于快速计算机模型仿真的缩放Vecchia近似
Scaled Vecchia approximation for fast computer-model emulation
摘要：
许多科学现象都是使用计算机实验来研究的，这些实验由计算机模型的多次运行组成，同时改变输入设置。高斯过程（GP）是计算机实验分析的流行工具，可以在输入设置之间进行插值，但对于大型数据集，直接GP推理在计算上是不可行的。我们适应和扩展了强大的一类GP方法从空间统计学，使大型计算机实验的可扩展性分析和仿真。具体来说，我们在变换的输入空间中应用Vecchia的有序条件近似，每个输入根据它与计算机模型响应的关系有多强进行缩放。通过使用Fisher评分估计GP协方差函数中的参数，从数据中学习缩放。我们的方法具有高度可扩展性，能够在模型运行次数接近线性的时间内进行估计、联合预测和模拟。在几个数值例子中，我们的方法大大优于现有的方法。
英文摘要：
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.
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