Global Sensitivity Analysis via Optimal Transport.

This article develops a novel approach to global sensitivity analysis for multivariate model outputs using the theory of optimal transport (OT). It introduces OT-based sensitivity indices grounded in both the classical Kantorovich formulation and the entropic regularization of OT, proving that classical OT-based indices satisfy key properties such as zero-independence (index equals zero if and only if input and output are independent), max-functionality (index is maximal under deterministic dependence), and monotonicity with respect to information refinement. The indices generalize Wagner’s variance-based sensitivity measures and decompose the input’s impact into advective (mean-related), diffusive (variance-related), and higher-order components, providing deeper insights into input-output relationships. The paper also proposes a computationally efficient given-data estimation strategy, validates it through numerical experiments including the Ishigami function and a large-scale linear Gaussian model, and applies the methodology to an assemble-to-order (ATO) simulator, demonstrating differences in input importance when analyzing univariate profit versus multivariate inventory outputs. The work highlights the advantages and limitations of entropic OT-based indices, particularly their tendency to lose discriminatory power as the regularization parameter grows, and suggests future research directions linking OT-based sensitivity analysis with advances in machine learning and kernel methods.