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题目：Efficient semi-supervised inference for logistic regression under case-control studies

报告人：郁文 教授 （复旦大学管理学院）

时间：2021年11月19日上午10：00-11：00

地点：腾讯会议  会议ID: 155 111 071

Abstract:

Semi-supervised learning has received increasingly attention in statistics and machine learning. In semi-supervised learning settings, a labeled data set with both outcomes and covariates and an unlabeled data set with covariates only are collected. We consider semi-supervised learning problem where the outcome in the labeled data is binary and the labeled data is collected by case-control sampling. Case-control sampling is an effective sampling scheme for alleviating imbalance structure in binary data. Under the logistic model assumption, case-control data can still provide consistent estimator for the slope parameter of the logistic regression model. However, the intercept parameter is not identifiable. Consequently, the marginal case proportion cannot be estimated from case-control data. We find out that with the availability of the unlabeled data, the intercept parameter can be identified in semi-supervised learning setting. We construct the likelihood function of the observed labeled and unlabeled data and obtain the maximum likelihood estimator via an iterative algorithm. The proposed estimator is shown to be consistent, asymptotically normal, and semiparametrically efficient. Extensive simulation studies are conducted to show the finite sample performance of the proposed method. The results imply that the unlabeled data not only helps to identify the intercept but also improves the estimation efficiency of the slope parameter. Meanwhile, the marginal case proportion can be estimated accurately by the proposed method.

报告人简介：

郁文，复旦大学管理学院统计学系教授，统计与数据科学系系主任。主要从事生存分析、两阶段抽样设计、半监督推断等研究，在国内外学术期刊发表论文二十余篇，主持多项国家自然科学基金、教育部博士点基金等研究工作。

联系人：胡涛

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