样本观测效应：枚举、随机化与泛化
Sample Observed Effects: Enumeration, Randomization and Generalization
AI总结：
针对因果效应反事实定义缺乏泛化性的问题，提出干预效应外部有效性的组合定义，基于背景集合制定泛化条件，用组合框架审视反事实公式问题，替代参数估计并展示在COVID-19问题中的应用。
摘要：
广泛使用的因果效应“反事实”定义是为无偏性和准确性推导的，而非泛化性。我们提出干预效应外部有效性（EV）的组合定义。首先定义效应观测“背景”的概念，然后基于样本的（观测与未观测）背景集合制定效应泛化的条件。这揭示了效应泛化的两个限度：（1）当变量的效应在其所有可枚举背景下被观测时；（2）当背景已充分随机化时。我们使用所得的组合框架重新审视原始反事实公式中的几个问题：样本外有效性、多效应的并发估计、偏差-方差权衡、统计功效，以及与当前预测和解释技术的联系。在方法上，这些定义还允许我们用非实验样本中的组合枚举和随机化问题替代反事实定义后的参数估计问题。我们使用所得的非参数框架证明流行的监督、解释和因果效应估计器性能中的（外部有效性、无混杂性和精确性）权衡。我们还说明该方法如何允许在非独立同分布样本中使用监督和解释方法。COVID-19大流行凸显了学习解决方案在严重不完整样本中提供预测的需求，我们展示了在这一紧迫问题中的应用。
英文摘要：
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.
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