A Generalized Kernel Method for Global Sensitivity Analysis

Global sensitivity analysis (GSA) is frequently used to analyze how the uncertainty in input parameters of computational models or in experimental setups influences the uncertainty of an output. Here we describe a class of GSA measures based on the embedding of the multiple output's joint probability distribution into a reproducing kernel Hilbert space (RKHS). In particular, the distance between embeddings is measured utilizing the maximum mean discrepancy, which has several key advantages over many common sensitivity measures. First, the proposed methodology defines measures for an arbitrary type of output, while maintaining easy computability for high-dimensional outputs. Second, by utilizing different kernels, or RKHSs, one can determine how the input parameters influence different features of the output distribution. This new class of sensitivity analysis measures, encapsulated into what are called beta(k)-indicators, are shown to contain both moment-independent and moment-based measures as special cases. The specific beta(k)-indicator arises from the particular choice of kernel. This analysis includes deriving new GSA measures as well as showing that certain previously proposed GSA measures, such as the variance-based indicators, are special cases of the beta(k)-indicators. Some basic test cases are used to showcase that the beta(k)-indicator derived from kernel-based GSA provides flexible tools capable of assessing a broad range of applications.

Automated summary

This paper describes a method for global sensitivity analysis based on embedding the joint probability distribution of multiple outputs into RKHS and measuring the distance between embeddings using maximum mean discrepancy. This method has the advantage of easy computability for high-dimensional outputs and determining the influence of input parameters on different features.