In causal inference, many estimands of interest can be expressed as a linear functional of the outcome regression function; this includes, for example, average causal effects of static, dynamic and stochastic interventions. For learning such estimands, in this work, we propose novel debiased machine learning estimators that are doubly robust asymptotically linear, thus providing not only doubly robust consistency but also facilitating doubly robust inference (e.g., confidence intervals and hypothesis tests). To do so, we first establish a key link between calibration, a machine learning technique typically used in prediction and classification tasks, and the conditions needed to achieve doubly robust asymptotic linearity. We then introduce calibrated debiased machine learning (C-DML), a unified framework for doubly robust inference, and propose a specific C-DML estimator that integrates cross-fitting, isotonic calibration, and debiased machine learning estimation. A C-DML estimator maintains asymptotic linearity when either the outcome regression or the Riesz representer of the linear functional is estimated sufficiently well, allowing the other to be estimated at arbitrarily slow rates or even inconsistently. We propose a simple bootstrap-assisted approach for constructing doubly robust confidence intervals. Our theoretical and empirical results support the use of C-DML to mitigate bias arising from the inconsistent or slow estimation of nuisance functions.

翻译：在因果推断中，许多感兴趣的估计量可以表示为结果回归函数的线性泛函；这包括例如静态、动态和随机干预的平均因果效应。针对此类估计量的学习，本文提出了一种新颖的去偏机器学习估计器，该估计器具有双重稳健的渐近线性性质，从而不仅提供双重稳健的一致性，还便于进行双重稳健的推断（例如置信区间和假设检验）。为此，我们首先建立了校准（一种通常用于预测和分类任务的机器学习技术）与实现双重稳健渐近线性所需条件之间的关键联系。随后，我们引入了校准去偏机器学习（C-DML），一个用于双重稳健推断的统一框架，并提出了一种特定的C-DML估计器，该估计器整合了交叉拟合、等渗校准和去偏机器学习估计。当结果回归或线性泛函的Riesz表示子中任意一个被充分准确地估计时，C-DML估计器能保持渐近线性，允许另一个以任意慢的速率甚至不一致地被估计。我们提出了一种简单的自助法辅助方法来构建双重稳健置信区间。我们的理论和实证结果支持使用C-DML来减轻由辅助函数估计不一致或缓慢引起的偏差。