A Generalized Kernel Method for Global Sensitivity Analysis

Kernel-based Global Sensitivity Analysis Obtained from a Single Data Set

“…Recently, kernel-based procedures have been proposed for GSA, which have distinct advantages over many traditional approaches [20,21,22]. First, kernel GSA defines sensitivity measures for arbitrary types of input-output domains, giving methodologies that are valid for dealing with different types of data.…”

“…First, kernel GSA defines sensitivity measures for arbitrary types of input-output domains, giving methodologies that are valid for dealing with different types of data. This has been demonstrated on systems with categorical, stochastic, time-series, functional and multivariate data [20,22]. Second, the calculation of kernel sensitivity indices relies on a technique known as the kernel embedding of distributions, which has been established to converge independent of the dimensionality of the output data [23].…”

“…Second, the calculation of kernel sensitivity indices relies on a technique known as the kernel embedding of distributions, which has been established to converge independent of the dimensionality of the output data [23]. Thus, the corresponding GSA methods remain computationally feasible for systems with high-dimensional outputs [23,20]. Third, kernel GSA is goal-oriented, with the underlying potential of tuning the analysis to the desired goals.…”

“…There are two known strategies for kernel-based GSA. One approach makes use of the maximum mean discrepancy (MMD) as a distance metric between the unconditional and conditional output distributions [20,22]. Another technique relies on the Hilbert-Schmidt independence criterion (HSIC) as a distance metric between the joint input-output distribution and the product of their marginals [21,22].…”

“…Another technique relies on the Hilbert-Schmidt independence criterion (HSIC) as a distance metric between the joint input-output distribution and the product of their marginals [21,22]. Recent studies have compared these two approaches and discussed the different advantages and insights they can provide [20,22]. This work, focuses on the MMD method when only a single set of input-output data is available for analysis, assuming an adequate sample size; this issue will be explored in an illustration in Section 4.2.…”