Kernel-based global sensitivity analysis obtained from a single data set

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.

Automated summary

This paper presents a new kernel-based global sensitivity analysis (GSA) tool for single input-output data sets, with three key advances: (1) a new numerical estimator that shows empirical improvement over previous procedures; (2) a computational method for generating inner statistical functions from a single data set; (3) a theoretical extension defining conditional sensitivity indices for capturing shared information about the output when input-input correlations exist. Utilizing these indices, a decomposition of output uncertainty based on optimal learning sequence of input variables is derived, remaining consistent with input correlations. The new methodology is validated on benchmark systems, providing valuable insights.