论文标题

半监督和高维设置中治疗效应估计的一般框架

A General Framework for Treatment Effect Estimation in Semi-Supervised and High Dimensional Settings

论文作者

Chakrabortty, Abhishek, Dai, Guorong

论文摘要

在本文中,我们旨在提供对治疗效果的半监督(SS)因果推论的一般和完整的理解。具体而言,我们考虑了两个这样的估计值:(a)平均治疗效果,以及(b)在SS环境中的原型情况,以两个可用的数据集为特征:(i)标记为大小$ n $的数据集,为响应提供了观察结果,可以观察到一组高尺寸的互助治疗指标,以及二型治疗指标; (ii)一个尺寸$ n $的未标记数据集,大于$ n $,但没有观察到响应。使用这两个数据集,我们开发了一个SS估计量的家族,该家族的确保为:(1)仅基于标记的数据集比其监督对应物更稳健和效率。除了可以通过监督方法获得的“标准”双重鲁棒性结果(在一致性方面)之外,只要正确指定模型中的倾向分数,我们就进一步建立了我们SS估计量的根N一致性和SS估计量的渐近正态性,而无需涉及涉及的nuiisance功能的特定形式。鲁棒性的这种改善是由于使用大量未标记的数据而产生的,因此在纯监督的环境中通常无法实现。此外,只要正确指定了所有滋扰函数,我们的估计器被证明是半参数有效的。此外,作为滋扰估计量的说明,我们考虑了涉及未知协变量转换机制的逆概率加权型核平滑估计器,并在高维场景中建立了新的成果,以均匀的收敛速率成果,这应该是独立的。关于模拟和实际数据的数值结果验证了我们的方法比其稳健性和效率相对于其监督的优势。

In this article, we aim to provide a general and complete understanding of semi-supervised (SS) causal inference for treatment effects. Specifically, we consider two such estimands: (a) the average treatment effect and (b) the quantile treatment effect, as prototype cases, in an SS setting, characterized by two available data sets: (i) a labeled data set of size $n$, providing observations for a response and a set of high dimensional covariates, as well as a binary treatment indicator; and (ii) an unlabeled data set of size $N$, much larger than $n$, but without the response observed. Using these two data sets, we develop a family of SS estimators which are ensured to be: (1) more robust and (2) more efficient than their supervised counterparts based on the labeled data set only. Beyond the 'standard' double robustness results (in terms of consistency) that can be achieved by supervised methods as well, we further establish root-n consistency and asymptotic normality of our SS estimators whenever the propensity score in the model is correctly specified, without requiring specific forms of the nuisance functions involved. Such an improvement of robustness arises from the use of the massive unlabeled data, so it is generally not attainable in a purely supervised setting. In addition, our estimators are shown to be semi-parametrically efficient as long as all the nuisance functions are correctly specified. Moreover, as an illustration of the nuisance estimators, we consider inverse-probability-weighting type kernel smoothing estimators involving unknown covariate transformation mechanisms, and establish in high dimensional scenarios novel results on their uniform convergence rates, which should be of independent interest. Numerical results on both simulated and real data validate the advantage of our methods over their supervised counterparts with respect to both robustness and efficiency.

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