Rethinking Robustness in Machine Learning: A Posterior Agreement Approach

The robustness of algorithms against covariate shifts is a fundamental problem with critical implications for the deployment of machine learning algorithms in the real world. Current evaluation methods predominantly measure robustness through the lens of standard generalization, relying on task performance measures like accuracy. This approach lacks a theoretical justification and underscores the need for a principled foundation of robustness assessment under distribution shifts. In this work, we set the desiderata for a robustness measure, and we propose a novel principled framework for the robustness assessment problem that directly follows the Posterior Agreement (PA) theory of model validation. Specifically, we extend the PA framework to the covariate shift setting and propose a measure for robustness evaluation. We assess the soundness of our measure in controlled environments and through an empirical robustness analysis in two different covariate shift scenarios: adversarial learning and domain generalization. We illustrate the suitability of PA by evaluating several models under different nature and magnitudes of shift, and proportion of affected observations. The results show that PA offers a reliable analysis of the vulnerabilities in learning algorithms across different shift conditions and provides higher discriminability than accuracy-based measures, while requiring no supervision.