论文标题
快速计算机模拟的尺度维奇亚近似
Scaled Vecchia approximation for fast computer-model emulation
论文作者
论文摘要
使用由计算机模型的多个运行组成的计算机实验研究了许多科学现象，同时改变了输入设置。高斯过程（GPS）是用于分析计算机实验的流行工具，可以在输入设置之间进行插值，但是直接的GP推理对于大型数据集来说是计算上不可行的。我们将强大的GP方法从空间统计数据进行调整并扩展，以实现大型计算机实验的可扩展分析和仿真。具体而言，我们将Vecchia的有序条件近似应用于变换后的输入空间，每个输入都根据其与计算机模型响应的密切相关。通过使用Fisher评分来估算GP协方差函数中的参数，从数据中学到了缩放。我们的方法是高度可扩展的，在模型运行次数中，在接近线性的时间内具有估计，关节预测和仿真。在几个数值示例中，我们的方法基本上优于现有方法。
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.
