报告题目: Matrix Completion with Covariate Information

　　报告人: 陈松蹊 教授 北京大学

　  报告时间: 2019.07.11(周四)下午16:00--17:00

　　报告地点: 新大楼1217报告厅

　　摘要: This paper investigates the problem of matrix completion from corrupted data, when additional covariates are available. Despite being seldomly considered in the matrix completion literature, these covariates often provide valuable information for completing the unobserved entries of the high-dimensional target matrix A0. Given a covariate matrix X with its rows representing the row covariates of A0, we consider a column-space-decomposition model A0 = X beta0+B0 where beta0 is a coefficient matrix and B0 is a low-rank matrix orthogonal to X in terms of column space. This model facilitates a clear separation between the interpretable covariate effects (X beta0) and the flexible hidden factor effects (B0). 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 A0 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.

　　报告人介绍: 陈松蹊，国家特聘专家，北京大学讲席教授，北京大学统计科学中心联席主任。他是美国科学促进会会员，数理统计学会资深会员，美国统计学会会员，国际统计学会当选会员，国际数理统计学会(IMS) 理事会常务理事。同时担任The Annals of Statistics编委（2010-2019年），美国统计学会会刊编委（自2018年），Environmentrics编委（自2018年）。自2015年他的团队在评估中国北方地区大气污染的变化，提出了去除气象干扰的方法，已经发布六份空气质量报告。目前主持国家重点研发专项项目“空气质量统计诊断模型”，两项自科基金重点项目。