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Robustness studies of black-box models is recognized as a necessary task fornumerical models based on structural equations and predictive models learnedfrom data. These studies must assess the model's robustness to possiblemisspecification of regarding its inputs (e.g., covariate shift). The study ofblack-box models, through the prism of uncertainty quantification (UQ), isoften based on sensitivity analysis involving a probabilistic structure imposedon the inputs, while ML models are solely constructed from observed data. Ourwork aim at unifying the UQ and ML interpretability approaches, by providingrelevant and easy-to-use tools for both paradigms. To provide a generic andunderstandable framework for robustness studies, we define perturbations ofinput information relying on quantile constraints and projections with respectto the Wasserstein distance between probability measures, while preservingtheir dependence structure. We show that this perturbation problem can beanalytically solved. Ensuring regularity constraints by means of isotonicpolynomial approximations leads to smoother perturbations, which can be moresuitable in practice. Numerical experiments on real case studies, from the UQand ML fields, highlight the computational feasibility of such studies andprovide local and global insights on the robustness of black-box models toinput perturbations.

Quantile-constrained Wasserstein projections for robust interpretability of numerical and machine learning models