Many algorithms have been recently proposed for causal machine learning. Yet, there is little to no theory on their quality, especially considering finite samples. In this work, we propose a theory based on generalization bounds that provides such guarantees. By introducing a novel change-of-measure inequality, we are able to tightly bound the model loss in terms of the deviation of the treatment propensities over the population, which we show can be empirically limited. Our theory is fully rigorous and holds even in the face of hidden confounding and violations of positivity. We demonstrate our bounds on semi-synthetic and real data, showcasing their remarkable tightness and practical utility.

翻译：近期有多种算法被提出用于因果机器学习，然而关于其质量的理论分析仍十分匮乏，尤其在有限样本情形下。本文基于泛化界理论提出了此类保证方法。通过引入一种新颖的测度变换不等式，我们能够根据总体中处理倾向的偏差紧密约束模型损失，并证明该偏差可在经验上被有效限制。我们的理论具有完全严谨性，即便在面对隐式混杂和阳性假设违反时依然成立。我们在半合成数据与真实数据上验证了所提泛化界的显著紧致性与实际效用。