Abstract Many methods for modeling functions over high-dimensional spaces assume global smoothness properties; such assumptions are often violated in practice. We introduce a method for modeling functions that display heterogeneity or contain discontinuities. The heterogeneity is dealt with by using a combination of Voronoi tessellation, to partition the input space, and separate Gaussian processes to model the function over different regions of the partitioned space. The proposed method is highly flexible since it allows the Voronoi cells to combine to form regions, which enables nonconvex and disconnected regions to be considered. In such problems, identifying the borders between regions is often of great importance and we propose an adaptive sampling method to gain extra information along such borders. The method is illustrated by simulated examples and an application to real data, in which we see improvements in prediction error over the commonly used stationary Gaussian process and other nonstationary variations. In our application, a computationally expensive computer model that simulates the formation of clouds is investigated, the proposed method more accurately predicts the underlying process at unobserved locations than existing emulation methods. Supplementary materials for this article are available online.

中文翻译：

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使用 Voronoi 镶嵌对异质性和不连续性进行高斯过程建模

摘要 许多在高维空间上建模函数的方法都假设全局平滑性；这些假设在实践中经常被违反。我们介绍了一种对显示异质性或包含不连续性的函数进行建模的方法。通过使用 Voronoi 镶嵌的组合来处理异质性，以分割输入空间，并通过分离高斯过程来对分割空间的不同区域上的函数进行建模。所提出的方法非常灵活，因为它允许 Voronoi 单元组合形成区域，从而可以考虑非凸区域和不连续区域。在这些问题中，识别区域之间的边界通常非常重要，我们提出了一种自适应采样方法来沿这些边界获取额外信息。该方法通过模拟示例和实际数据的应用来说明，其中我们看到与常用的平稳高斯过程和其他非平稳变化相比，预测误差有所改善。在我们的应用程序中，研究了一个计算成本高的计算机模型来模拟云的形成，所提出的方法比现有的模拟方法更准确地预测未观察到的位置的潜在过程。本文的补充材料可在线获取。与现有的仿真方法相比，所提出的方法更准确地预测了未观察到的位置的潜在过程。本文的补充材料可在线获取。与现有的仿真方法相比，所提出的方法更准确地预测了未观察到的位置的潜在过程。本文的补充材料可在线获取。