主题：高维数据矩阵填补

主讲人：北京大学 陈松蹊教授

主持人：统计学院 郭斌副教授

时间：2019年4月9日（星期二）上午11:00-12:00

地点：西南财经大学柳林校区弘远楼408会议室

主办单位：统计研究中心 统计学院 科研处

主讲人简介：

陈松蹊，北京大学教授，现任北京大学光华管理学院商务统计与经济计量系联合系主任、北京大学统计科学中心联席主任。他是数理统计学会(Institute of Mathematical Statistics)资深会员（fellow)，美国统计学会会士（fellow），国际统计学会(International Statistics Institute)当选会员 （elected member），数理统计学会(IMS)理事会常务理事( Council member)，2018年11月，陈松蹊教授当选世界知名学术组织-美国科学促进会会士（AAAS Fellow）,成为当年入选“统计学专业分会”的7位会员之一。主要研究领域：环境统计、大气污染数据分析、经济、金融计量学、风险度量、统计学在人口普查中的应用、随机过程统计推断、高维数据分析、抽样方法，先后发表高水平研究论文88篇。先后担任统计学顶级期刊The Annals of Statistics，Journal of the American Statistical Association，Journal of Business and Economic Statistics的副主编, Statistics and Its Interface的联席主编。在加入北京大学光华管理学院之前，陈松蹊教授是美国爱荷华州立大学统计系终身教授。

主要内容：

This paper investigates the problem of matrix completion from corrupted data, when additional covariates are available. Despite being seldom considered in the matrix completion literature, these covariates often provide valuable information for completing the unobserved entries of the high-dimensional target matrix A. Given a covariate matrix $X$ with its rows representing the row covariates of A, we consider a column-space-decomposition model A=X \beta+B where \beta is a coefficient matrix and $B$ is a low-rank matrix orthogonal to X in terms of column space. This model facilitates a clear separation between the interpretable covariate effects and the flexible hidden factor effects. Besides, our work allows the probabilities of observation to depend on the covariate matrix, and hence a missing-at-random mechanism is permitted. We propose a novel penalized estimator for A by utilizing both Frobenius-norm and nuclear-norm regularizations with an efficient and scalable algorithm. Asymptotic convergence rates of the proposed estimators are studied. The empirical performance of the proposed methodology is illustrated via both numerical experiments and a real data application.