  Robustness studies of black-box models is recognized as a necessary task for
numerical models based on structural equations and predictive models learned
from data. These studies must assess the model's robustness to possible
misspecification of regarding its inputs (e.g., covariate shift). The study of
black-box models, through the prism of uncertainty quantification (UQ), is
often based on sensitivity analysis involving a probabilistic structure imposed
on the inputs, while ML models are solely constructed from observed data. Our
work aim at unifying the UQ and ML interpretability approaches, by providing
relevant and easy-to-use tools for both paradigms. To provide a generic and
understandable framework for robustness studies, we define perturbations of
input information relying on quantile constraints and projections with respect
to the Wasserstein distance between probability measures, while preserving
their dependence structure. We show that this perturbation problem can be
analytically solved. Ensuring regularity constraints by means of isotonic
polynomial approximations leads to smoother perturbations, which can be more
suitable in practice. Numerical experiments on real case studies, from the UQ
and ML fields, highlight the computational feasibility of such studies and
provide local and global insights on the robustness of black-box models to
input perturbations.
