Estimating causal quantities from observational data is crucial for understanding the safety and effectiveness of medical treatments. However, to make reliable inferences, medical practitioners require not only estimating averaged causal quantities, such as the conditional average treatment effect, but also understanding the randomness of the treatment effect as a random variable. This randomness is referred to as aleatoric uncertainty and is necessary for understanding the probability of benefit from treatment or quantiles of the treatment effect. Yet, the aleatoric uncertainty of the treatment effect has received surprisingly little attention in the causal machine learning community. To fill this gap, we aim to quantify the aleatoric uncertainty of the treatment effect at the covariate-conditional level, namely, the conditional distribution of the treatment effect (CDTE). Unlike average causal quantities, the CDTE is not point identifiable without strong additional assumptions. As a remedy, we employ partial identification to obtain sharp bounds on the CDTE and thereby quantify the aleatoric uncertainty of the treatment effect. We then develop a novel, orthogonal learner for the bounds on the CDTE, which we call AU-learner. We further show that our AU-learner has several strengths in that it satisfies Neyman-orthogonality and is doubly robust. Finally, we propose a fully-parametric deep learning instantiation of our AU-learner.

翻译：从观测数据中估计因果量对于理解医疗治疗的安全性和有效性至关重要。然而，为了进行可靠的推断，医疗从业者不仅需要估计平均因果量（如条件平均处理效应），还需要理解作为随机变量的治疗效果的随机性。这种随机性被称为偶然不确定性，对于理解治疗获益的概率或治疗效应的分位数是必要的。然而，治疗效果的偶然不确定性在因果机器学习社区中受到的关注出人意料地少。为了填补这一空白，我们旨在量化协变量条件层面下治疗效果的偶然不确定性，即治疗效应的条件分布。与平均因果量不同，在没有强额外假设的情况下，治疗效应的条件分布不是点可识别的。作为补救措施，我们采用部分识别来获得治疗效应条件分布的尖锐界，从而量化治疗效果的偶然不确定性。随后，我们开发了一种新颖的、用于治疗效应条件分布界的正交学习器，我们称之为AU学习器。我们进一步证明，我们的AU学习器具有若干优势，即满足Neyman正交性且具有双重稳健性。最后，我们提出了AU学习器的一个完全参数化的深度学习实例化。