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

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 first-order and total HSIC sensitivity indices, which are bounded, interpretable, and moment-independent analogues to the first-order and total-effect Sobol' indices, respectively. 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 first-order and total HSIC sensitivity indices are demonstrated through computational experiments on models that feature nonlinear relationships, correlated inputs, and functional outputs.

25 pages, revised article