深圳大学数学科学学院

荔园学者Colloquium第一百一十期

讲座题目: Precision matrix regularization for ultra-high dimensional data

主讲人：潘建新 教授（北京师范大学）

讲座时间：2024年12月14日上午9:00-9:40

讲座地点：深圳大学粤海校区汇星楼三号报告厅

内容摘要：A method that estimates the precision matrix of a great number of variables in the extreme scope of “ultra-high dimension” and “small sample-size” is proposed. First, a covariance column-wise screening method is provided in order to identify a small sub-group that are significantly correlated, from thousands and even millions of variables. Second, a regularization of block-diagonal covariance structure of the thousands or millions of variables is developed, in which only covariances of the variables in the small sub-group are retained and all others vanish. Third, it is further showed that under certain mild conditions the vital sub-group identified by the proposed method is consistent. A major advantage of the proposed method is its computational efficiency, as it produces a reliable precision matrix estimator for thousands of variables within a few of seconds, while the existing methods take at least several hours and even though they still yield inaccurate estimators. Empirical data studies and numerical simulations, which will be demonstrated by our developed R software package, show that the proposed precision matrix estimation substantially outperforms existing methods in the sense of much less computing time and much more accurate estimation for ultrahigh dimensional data.

主讲人简介：潘建新，北京师范大学和北京师范大学-香港浸会大学联合国际学院(UIC)讲座教授，国家高层次人才计划特聘专家, UIC 副校长（研究与拓展）, 广东省数据科学与技术交叉应用重点实验室主任。在统计学及交叉学科期刊上发表学术论文 140余篇，出版学术专著 3 部。潘教授是英国皇家统计学会会士（RSS Fellow）、国际统计学会选举会员、英国数据科学与人工智能研究院图灵研究员， 曾任英国曼彻斯特大学终身教授、概率统计系系主任、英国皇家统计学会曼彻斯特分会主席。是 Biometrics , Journal of Multivariate Analysis, Biometrical Journal, Electronic Journal of Statistics 等多个统计学期刊编委。

欢迎师生参加！

邀请人：数学科学学院（周彦）

                                   　数学科学学院

　　　　　　　　　　　　　　　　 2024年12月13日