The widely used 'Counterfactual' definition of Causal Effects was derived for unbiasedness and accuracy - and not generalizability. We propose a Combinatorial definition for the External Validity (EV) of intervention effects. We first define the concept of an effect observation 'background'. We then formulate conditions for effect generalization based on samples' sets of (observed and unobserved) backgrounds. This reveals two limits for effect generalization: (1) when effects of a variable are observed under all their enumerable backgrounds, or, (2) when backgrounds have become sufficiently randomized. We use the resulting combinatorial framework to re-examine several issues in the original counterfactual formulation: out-of-sample validity, concurrent estimation of multiple effects, bias-variance tradeoffs, statistical power, and connections to current predictive and explaining techniques. Methodologically, the definitions also allow us to replace the parametric estimation problems that followed the counterfactual definition by combinatorial enumeration and randomization problems in non-experimental samples. We use the resulting non-parametric framework to demonstrate (External Validity, Unconfoundness and Precision) tradeoffs in the performance of popular supervised, explaining, and causal-effect estimators. We also illustrate how the approach allows for the use of supervised and explaining methods in non-i.i.d. samples. The COVID19 pandemic highlighted the need for learning solutions to provide predictions in severally incomplete samples. We demonstrate applications in this pressing problem.

翻译：广泛使用的因果效应"反事实"定义旨在保证无偏性和准确性，而非可泛化性。我们提出了一种针对干预效应外部有效性（EV）的组合定义。首先定义了效应观测"背景"的概念，随后基于样本的（已观测与未观测）背景集合构建了效应泛化条件。这揭示了效应泛化的两个极限：(1)当变量的效应在所有可枚举背景下均被观测时；(2)当背景达到充分随机化时。我们运用所得组合框架重新审视原始反事实公式中的若干问题：样本外有效性、多重效应的并发估计、偏差-方差权衡、统计功效，以及与当前预测解释技术的关联。方法论上，该定义使我们能够将反事实定义衍生的参数估计问题，转化为非实验样本中的组合枚举与随机化问题。我们利用所得非参数框架展示了常用监督学习、解释模型与因果效应估计器在（外部有效性、无混淆性与精确度）权衡中的性能表现，并阐明该方法如何允许在非独立同分布样本中使用监督与解释方法。COVID19大流行凸显了在严重不完整样本中提供预测的学习方案需求，我们展示了该方法在这一紧迫问题中的应用实例。