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.

翻译：我们提出了一种新颖的估计器，用于在不同分布环境下存在隐藏混杂因素时预测结果，且无需依赖正则化或已知的因果结构。该方法基于对协变量与响应噪声之间依赖关系的参数化建模，确保了最优预测性能与良好的渐近性质。我们在具有直接经验对应性的简约假设下实现了可识别性，从而能够将因果参数整合到一个生成模型中，该模型能够复现测试环境下真实的条件分布。此方法在干预条件下实现了与测试分布的概率对齐，无需进行最坏情况优化或对测试时扰动强度作特定假设，即可提供稳健的预测。我们的研究结果代表了因果性统计理解的重要进展，为不同领域的预测建模提供了一个稳健而灵活的框架。