The accessibility of vast volumes of unlabeled data has sparked growing interest in semi-supervised learning (SSL) and covariate shift transfer learning (CSTL). In this paper, we present an inference framework for estimating regression coefficients in conditional mean models within both SSL and CSTL settings, while allowing for the misspecification of conditional mean models. We develop an augmented inverse probability weighted (AIPW) method, employing regularized calibrated estimators for both propensity score (PS) and outcome regression (OR) nuisance models, with PS and OR models being sequentially dependent. We show that when the PS model is correctly specified, the proposed estimator achieves consistency, asymptotic normality, and valid confidence intervals, even with possible OR model misspecification and high-dimensional data. Moreover, by suppressing detailed technical choices, we demonstrate that previous methods can be unified within our AIPW framework. Our theoretical findings are verified through extensive simulation studies and a real-world data application.

翻译：海量未标记数据的可获取性激发了学界对半监督学习与协变量偏移迁移学习的日益关注。本文提出了一种推断框架，用于在半监督学习和协变量偏移迁移学习两种设定下估计条件均值模型的回归系数，同时允许条件均值模型存在误设。我们开发了一种增强逆概率加权方法，采用正则化校准估计量分别处理倾向得分模型与结果回归模型这两个干扰模型，且二者具有序列依赖性。我们证明：当倾向得分模型设定正确时，即使结果回归模型可能存在误设且数据为高维情形，所提估计量仍具有一致性、渐近正态性并能构造有效的置信区间。此外，通过简化具体技术细节的讨论，我们论证了现有方法均可统一于本研究的增强逆概率加权框架中。理论结果通过大量模拟研究与实际数据应用得到了验证。