论文标题
从单个数据集获得的基于内核的全局灵敏度分析
Kernel-based Global Sensitivity Analysis Obtained from a Single Data Set
论文作者
论文摘要
全球灵敏度分析（GSA）的结果通常指导对复杂输入输出系统的理解。最近，已经提出了基于内核的GSA方法，以处理其处理复杂系统范围的能力。在本文中，当仅一组输入输出数据可用时，我们会开发一组新的内核GSA工具。取得了三个关键的进步：（1）提出了一个新的数值估计器，以证明对先前程序的经验改善。 （2）提出了一种用于从单个数据集生成内部统计函数的计算方法。 （3）进行理论扩展以定义有条件的灵敏度指数，该指标揭示了当存在固有输入输入相关性时输入有关输出的共享信息的程度。利用这些条件灵敏度指标，根据所谓的输入变量的最佳学习顺序得出了输出不确定性的分解，当输入变量之间存在相关性时，该序列是一致的。尽管这些进步涵盖了一系列GSA主题，但通用的单个数据集数值解决方案是通过称为分布的条件平均嵌入的技术提供的。新方法是在基准系统上实施的，以证明提供的见解。
Results from global sensitivity analysis (GSA) often guide the understanding of complicated input-output systems. Kernel-based GSA methods have recently been proposed for their capability of treating a broad scope of complex systems. In this paper we develop a new set of kernel GSA tools when only a single set of input-output data is available. Three key advances are made: (1) A new numerical estimator is proposed that demonstrates an empirical improvement over previous procedures. (2) A computational method for generating inner statistical functions from a single data set is presented. (3) A theoretical extension is made to define conditional sensitivity indices, which reveal the degree that the inputs carry shared information about the output when inherent input-input correlations are present. Utilizing these conditional sensitivity indices, a decomposition is derived for the output uncertainty based on what is called the optimal learning sequence of the input variables, which remains consistent when correlations exist between the input variables. While these advances cover a range of GSA subjects, a common single data set numerical solution is provided by a technique known as the conditional mean embedding of distributions. The new methodology is implemented on benchmark systems to demonstrate the provided insights.
