论文标题
在分层抽样下半监督设置中预测规则的有效估计和评估
Efficient Estimation and Evaluation of Prediction Rules in Semi-Supervised Settings under Stratified Sampling
论文作者
论文摘要
在许多当代应用中,在标记的示例受到限制的同时,很容易获得大量未标记的数据。对于半监督学习(SSL),旨在利用未标记的数据来改善估计或预测。但是,当前的SSL文献主要集中在从感兴趣的人群中随机选择标记数据的设置。非随机抽样虽然提出了其他分析挑战,但非常适用于许多现实世界中的问题。此外,目前尚无用于估计非随机抽样下拟合模型的预测性能的SSL方法。在本文中,我们提出了一个两步SSL程序,用于评估基于布里尔评分和分层采样下的整体错误分类率的工作二进制回归模型的预测规则。在第I步中,我们通过具有非线性基础功能的加权回归将缺失的标签算,以说明非随机抽样并提高效率。在第II步中,我们扩大了初始归精,以确保所得估计器的一致性,而不管预测模型的规范或插补模型的规格如何。然后,通过增强归档来获得最终的估计器。我们提供渐近理论和数值研究,说明我们的建议在效率增长方面优于其监督对应物。我们的方法是由电子健康记录(EHR)研究激励的,并通过对基于EHR的糖尿病神经病研究的真实数据分析进行了验证。
In many contemporary applications, large amounts of unlabeled data are readily available while labeled examples are limited. There has been substantial interest in semi-supervised learning (SSL) which aims to leverage unlabeled data to improve estimation or prediction. However, current SSL literature focuses primarily on settings where labeled data is selected randomly from the population of interest. Non-random sampling, while posing additional analytical challenges, is highly applicable to many real world problems. Moreover, no SSL methods currently exist for estimating the prediction performance of a fitted model under non-random sampling. In this paper, we propose a two-step SSL procedure for evaluating a prediction rule derived from a working binary regression model based on the Brier score and overall misclassification rate under stratified sampling. In step I, we impute the missing labels via weighted regression with nonlinear basis functions to account for nonrandom sampling and to improve efficiency. In step II, we augment the initial imputations to ensure the consistency of the resulting estimators regardless of the specification of the prediction model or the imputation model. The final estimator is then obtained with the augmented imputations. We provide asymptotic theory and numerical studies illustrating that our proposals outperform their supervised counterparts in terms of efficiency gain. Our methods are motivated by electronic health records (EHR) research and validated with a real data analysis of an EHR-based study of diabetic neuropathy.