Double Robust Semi-Supervised Inference for the Mean: Selection Bias under MAR Labeling with Decaying Overlap
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重叠衰减与随机缺失标注选择偏差下的双重稳健半监督均值推断
- 研究问题
- 当未标注样本远多于已标注样本，且随机缺失标注机制存在选择偏差与重叠衰减时，如何对结果均值进行稳健推断？
- 方法与思路
- 作者提出双重稳健半监督均值估计量，刻画其渐近性质，并构造带偏置项的逻辑模型及分层标注模型估计衰减倾向得分。
- 材料陈述的贡献
- 摘要称任一辅助模型正确即可一致，两个模型均正确时可进行非标准速度推断，并扩展至处理组不平衡的因果推断。
- 阅读关注点
- 应核对随机缺失标注与重叠衰减的精确定义、收敛速度与标注样本量的关系，以及高维条件和双重稳健结论的适用范围。
- 阅读边界
- 这是 arXiv 预印本，未核实同行评审或期刊接收。摘要未给出重叠衰减速度、正则条件及方差构造，无法判断极少标注时的推断可靠性。
原文摘要
Semi-supervised (SS) inference has received much attention in recent years. Apart from a moderate-sized labeled data, L, the SS setting is characterized by an additional, much larger sized, unlabeled data, U. The setting of |U| >> |L|, makes SS inference unique and different from the standard missing data problems, owing to natural violation of the so-called "positivity" or "overlap" assumption. However, most of the SS literature implicitly assumes L and U to be equally distributed, i.e., no selection bias in the labeling. Inferential challenges in missing at random (MAR) type labeling allowing for selection bias, are inevitably exacerbated by the decaying nature of the propensity score (PS). We address this gap for a prototype problem, the estimation of the response's mean. We propose a double robust SS (DRSS) mean estimator and give a complete characterization of its asymptotic properties. The proposed estimator is consistent as long as either the outcome or the PS model is correctly specified. When both models are correctly specified, we provide inference results with a non-standard consistency rate that depends on the smaller size |L|. The results are also extended to causal inference with imbalanced treatment groups. Further, we provide several novel choices of models and estimators of the decaying PS, including a novel offset logistic model and a stratified labeling model. We present their properties under both high and low dimensional settings. These may be of independent interest. Lastly, we present extensive simulations and also a real data application.