In real-world scenarios, data collection limitations often result in partially labeled datasets, leading to difficulties in drawing reliable causal inferences. Traditional approaches in the semi-supervised (SS) and missing data literature may not adequately handle these complexities, leading to biased estimates. To address these challenges, our paper introduces a novel decaying missing-at-random (decaying MAR) framework. This framework tackles missing outcomes in high-dimensional settings and accounts for selection bias arising from the dependence of labeling probability on covariates. Notably, we relax the need for a positivity condition, commonly required in the missing data literature, and allow uniform decay of labeling propensity scores with sample size, accommodating faster growth of unlabeled data. Our decaying MAR framework enables easy rate double-robust (DR) estimation of average treatment effects, succeeding where other methods fail, even with correctly specified nuisance models. Additionally, it facilitates asymptotic normality under model misspecification. To achieve this, we propose adaptive new targeted bias-reducing nuisance estimators and asymmetric cross-fitting, along with a novel semi-parametric approach that fully leverages large volumes of unlabeled data. Our approach requires weak sparsity conditions. Numerical results confirm our estimators' efficacy and versatility, addressing selection bias and model misspecification.

翻译：现实场景中，数据收集局限性常导致部分标记数据集，进而引发可靠因果推断的困难。传统半监督（SS）与缺失数据文献中的方法难以充分应对这些复杂性，易产生有偏估计。为应对这些挑战，本文提出一种新颖的衰减随机缺失（decaying MAR）框架。该框架处理高维场景中的结果缺失问题，并考虑标记概率对协变量依赖性产生的选择偏差。值得注意的是，我们放宽了缺失数据文献中常见的正性条件要求，允许标记倾向得分随样本量均匀衰减，从而适应未标记数据的更快增长。所提出的衰减MAR框架可实现平均处理效应的速率双重稳健（DR）估计，即使在正确设定的干扰模型下，也能在其他方法失效时成功推断。此外，该框架在模型误设条件下仍能保证渐近正态性。为此，我们提出自适应新型靶向偏差缩减干扰估计器与非对称交叉拟合方法，并构建了能充分利用大规模未标记数据的新型半参数方法。本方法仅需弱稀疏条件。数值结果证实了我们的估计器在处理选择偏差与模型误设问题时的有效性与普适性。