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Environment-Adaptive Covariate Selection: Learning When to Use Spurious Correlations for Out-of-Distribution Prediction

A common approach to out-of-distribution prediction restricts models to causal or invariant covariates to avoid spurious associations that may change across environments. Despite its theoretical appeal, this strategy can underperform empirical risk minimization when only a subset of the causal parents of the outcome is observed. In such settings, non-causal covariates can serve as proxies for unobserved causal parents and improve prediction when the proxy relationship is stable, but they can hurt when shifts disrupt that relationship. Thus, the optimal covariate set can depend on the specific shift encountered. Because different shifts leave signatures in the unlabeled covariate distribution, we propose an environment-adaptive covariate selection algorithm that maps environment-level summaries to environment-specific covariate sets. These summaries may be hand-crafted or learned from multi-environment data, and prior causal knowledge can be incorporated as constraints. Across simulations and applied datasets, the proposed method improves over static causal, invariant, and other non-adaptive rules under diverse shifts.

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