主题：Semi-supervised learning using copula-based regression and model averaging
主讲人：西安交通大学喻达磊教授
主持人：统计与数据科学学院兰伟教授
时间：2026年10月23日（周五）下午15:00-16:00
地点：柳林校区弘远楼408会议室
主办单位：统计与数据科学学院和统计研究中心 科研处
主讲人简介：
喻达磊，西安交通大学数学与统计学院教授、博士生导师。他博士毕业于香港城市大学管理科学系，曾任职于云南财经大学，2023年2月起任教于西安交通大学。国家高层次人才计划及西安交通大学校内青拔A类支持计划入选者。
主要研究领域为统计预测、估计理论与统计极限理论，具体聚焦于模型选择、模型平均、混合效应模型及空间计量经济学的理论与应用。其研究成果发表于 JRSSB、JASA、JMLR、JBES、《中国科学：数学》等统计学与机器学习顶级期刊。主持三项国家自然科学基金项目，并主持一项国家重点研发项目课题。
内容提要：
The available data in semi-supervised learning usually consists of relatively small sized labeled data and much larger sized unlabeled data. How to effectively exploit unlabeled data is the key issue. In this paper, we write the regression function in the form of a copula and marginal distributions, and the unlabeled data can be exploited to improve the estimation of the marginal distributions. The predictions based on different copulas are weighted, where the weights are obtained by minimizing an asymptotically unbiased estimator of the prediction loss. Error-ambiguity decomposition of the prediction loss is performed such that unlabeled data can be exploited to improve the prediction loss estimation. We investigate the uniform nonasymptotic error bounds of copula parameter and regression function estimators of the candidate models under the semi-supervised framework, as well as the asymptotic optimality and weight consistency of the model averaging estimator. By incorporating unlabeled data into the candidate model estimation process, the semi-supervised method possesses tighter nonasymptotic error bounds over its supervised counterpart. In addition, our model averaging estimator leads to an improved upper bound on the convergence rate in asymptotic optimality and weight consistency than the supervised counterpart. Extensive simulation experiments and the California housing dataset demonstrate the effectiveness of the proposed method.
