In the partially-observed outcome setting, a recent set of proposals known as "prediction-powered inference" (PPI) involve (i) applying a pre-trained machine learning model to predict the response, and then (ii) using these predictions to obtain an estimator of the parameter of interest with asymptotic variance no greater than that which would be obtained using only the labeled observations. While existing PPI proposals consider estimators arising from M-estimation, in this paper we generalize PPI to any regular asymptotically linear estimator. Furthermore, by situating PPI within the context of an existing rich literature on missing data and semi-parametric efficiency theory, we show that while PPI does not achieve the semi-parametric efficiency lower bound outside of very restrictive and unrealistic scenarios, it can be viewed as a computationally-simple alternative to proposals in that literature. We exploit connections to that literature to propose modified PPI estimators that can handle three distinct forms of covariate distribution shift. Finally, we illustrate these developments by constructing PPI estimators of true positive rate, false positive rate, and area under the curve via numerical studies.

翻译：在部分观测结果设置中，最近一系列被称为"预测驱动推断"（PPI）的提案涉及（i）应用预训练的机器学习模型来预测响应，然后（ii）利用这些预测获得目标参数的估计量，其渐近方差不超过仅使用标记观测值所能获得的方差。虽然现有PPI提案考虑的是由M估计产生的估计量，但本文将PPI推广至任何正则渐近线性估计量。此外，通过将PPI置于缺失数据和半参数效率理论的现有丰富文献背景中，我们证明：除了在极其受限且不现实的场景外，PPI虽未达到半参数效率下界，但可被视为该文献中提案的计算简化替代方案。我们利用与该文献的理论联系，提出了能够处理三种不同协变量分布偏移形式的改进PPI估计量。最后，我们通过数值研究构建真实阳性率、假阳性率及曲线下面积的PPI估计量来阐释这些进展。