Abstract
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.
Funding Statement
Support from the ANR-3IA Artificial and Natural Intelligence Toulouse Institute is gratefully acknowledged.
Acknowledgments
The authors warmly thank the Associate Editor, Editor-In-Chief, and the three anonymous reviewers for their helpful remarks, as well as Jean-Bernard Lasserre (Institut de Mathématique de Toulouse) and Guillaume Dalle (CERMICS) for their help in solving the optimization problem at the heart of this work, Clément Bénesse (Institut de Mathématiques de Toulouse) and Antoine Paolini (UVSQ Université Paris Saclay) for their support on some of the mathematical aspects of this work.
Citation
Marouane Il Idrissi. Nicolas Bousquet. Fabrice Gamboa. Bertrand Iooss. Jean-Michel Loubes. "Quantile-constrained Wasserstein projections for robust interpretability of numerical and machine learning models." Electron. J. Statist. 18 (2) 2721 - 2770, 2024. https://doi.org/10.1214/24-EJS2268
Information