A new kernel-based index for the global sensitivity analysis of models with correlated inputs

TL;DR

This paper introduces a new kernel-based sensitivity index using HSIC for models with correlated and functional inputs and outputs, offering a bounded, interpretable, and moment-independent measure.

Contribution

The paper develops the total HSIC sensitivity index with a monotonicity property and provides an efficient algorithm for its empirical estimation, enhancing sensitivity analysis for complex models.

Findings

Effective in models with nonlinear relationships

Handles correlated and functional inputs/outputs

Reduces computational complexity

Abstract

We present an HSIC-based approach for global sensitivity analysis of broad classes of models with correlated and possibly function-valued inputs and outputs. To this end, we define the total HSIC sensitivity index: a bounded, interpretable, and moment-independent analogue to the total-effect Sobol' index. These desirable qualities hinge upon the key property of monotonicity under marginalization for the HSIC. We rigorously establish this monotonicity property by using a suitable class of augmented kernels. Furthermore, we provide an efficient algorithm for computing an empirical estimator of the HSIC that significantly reduces computational complexity and storage requirements. The effectiveness and interpretability of the total HSIC sensitivity indices are demonstrated through computational experiments on models that feature nonlinear relationships, correlated inputs, and functional outputs.