When Shift Happens - Confounding Is to Blame

Distribution shifts introduce uncertainty that undermines the robustness and generalization capabilities of machine learning models. While conventional wisdom suggests that learning causal-invariant representations enhances robustness to such shifts, recent empirical studies present a counterintuitive finding: (i) empirical risk minimization (ERM) can rival or even outperform state-of-the-art out-of-distribution (OOD) generalization methods, and (ii) OOD generalization performance improves when all available covariates, including non-causal ones, are utilized. We present theoretical and empirical explanations that attribute this phenomenon to hidden confounding. Shifts in hidden confounding induce changes in data distributions that violate assumptions commonly made by existing approaches. Under such conditions, we prove that generalization requires learning environment-specific relationships, rather than relying solely on invariant ones. Furthermore, we explain why models augmented with non-causal but informative covariates can mitigate the challenges posed by hidden confounding shifts. These findings offer new theoretical insights and practical guidance, serving as a roadmap for future research on OOD generalization and principled covariate-selection strategies.