  We introduce a novel estimator for predicting outcomes in the presence of
hidden confounding across different distributional settings without relying on
regularization or a known causal structure. Our approach is based on
parametrizing the dependence of the covariates with response noise, ensuring
optimal prediction and favorable asymptotic properties. We achieve
identifiability under lean assumptions that have direct empirical translation,
enabling the incorporation of causal parameters into a generative model that
replicates the true conditional distribution of a test environment. This method
achieves probabilistic alignment with test distributions uniformly across
interventions, offering robust predictions without the need for worst-case
optimization or specific assumptions about the strength of perturbations at
test. Our findings represent a significant advancement in the statistical
understanding of causality, providing a robust and flexible framework for
predictive modeling in varied domains.
