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

TL;DR

This paper introduces new kernel-based global sensitivity analysis tools designed for single data set scenarios, including improved estimators, methods for generating statistical functions, and theoretical extensions for understanding input correlations.

Contribution

The paper presents a novel kernel GSA framework with an improved estimator, a method for deriving statistical functions from one data set, and a theoretical extension for analyzing correlated inputs.

Findings

Empirical improvement of the new numerical estimator over previous methods.

Effective generation of inner statistical functions from a single data set.

Decomposition of output uncertainty using the optimal learning sequence.

Abstract

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.