摘要翻译：
给出一个因果图，DO-演算可以将治疗效果表示为可经验估计的观察联合分布的函数。有时do-calculus识别多个有效公式，促使我们比较相应估计量的统计性质。例如，后门公式在观察到所有混杂物时适用，而前门公式在观察到的中介传递因果效应时适用。在这篇论文中，我们研究了混淆因子和中介因子都被观测到的过度识别场景，使得两个估计量都是有效的。针对线性高斯因果模型，我们证明了任何一个估计量都可以通过一个无界常数因子来控制另一个估计量。其次，我们导出了一个最优估计量，它利用了所有的观测变量，并对其有限样本方差进行了约束。我们证明了它严格地优于后门和前门估计器，并且这种改进可以是无界的。我们还提出了一个组合两个数据集的过程，一个与观察到的混杂物，另一个与观察到的中介物。最后，我们在模拟数据以及IHDP和JTPA数据集上对我们的方法进行了评估。
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英文标题：
《Estimating Treatment Effects with Observed Confounders and Mediators》
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作者：
Shantanu Gupta, Zachary C. Lipton, David Childers
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最新提交年份：
2021
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分类信息：

一级分类：Statistics        统计学
二级分类：Methodology        方法论
分类描述：Design, Surveys, Model Selection, Multiple Testing, Multivariate Methods, Signal and Image Processing, Time Series, Smoothing, Spatial Statistics, Survival Analysis, Nonparametric and Semiparametric Methods
设计，调查，模型选择，多重检验，多元方法，信号和图像处理，时间序列，平滑，空间统计，生存分析，非参数和半参数方法
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一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Economics        经济学
二级分类：Econometrics        计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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一级分类：Statistics        统计学
二级分类：Machine Learning        机器学习
分类描述：Covers machine learning papers (supervised, unsupervised, semi-supervised learning, graphical models, reinforcement learning, bandits, high dimensional inference, etc.) with a statistical or theoretical grounding
覆盖机器学习论文（监督，无监督，半监督学习，图形模型，强化学习，强盗，高维推理等）与统计或理论基础
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英文摘要：
  Given a causal graph, the do-calculus can express treatment effects as functionals of the observational joint distribution that can be estimated empirically. Sometimes the do-calculus identifies multiple valid formulae, prompting us to compare the statistical properties of the corresponding estimators. For example, the backdoor formula applies when all confounders are observed and the frontdoor formula applies when an observed mediator transmits the causal effect. In this paper, we investigate the over-identified scenario where both confounders and mediators are observed, rendering both estimators valid. Addressing the linear Gaussian causal model, we demonstrate that either estimator can dominate the other by an unbounded constant factor. Next, we derive an optimal estimator, which leverages all observed variables, and bound its finite-sample variance. We show that it strictly outperforms the backdoor and frontdoor estimators and that this improvement can be unbounded. We also present a procedure for combining two datasets, one with observed confounders and another with observed mediators. Finally, we evaluate our methods on both simulated data and the IHDP and JTPA datasets.
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PDF链接：
https://arxiv.org/pdf/2003.11991