报告题目：Graphical Knockoff Filter for High-dimensional Regression Models

报告时间：11月29日，星期四，下午15：00—16：30

报告地点：北五楼319

报告人：李高荣，北京工业大学

报告摘要：

Controlling the false discovery rate (FDR) is a hot and challenging topic in the multiple hypothesis testing problems, especially for the high-dimensional regression models.  In this paper, the main aim is to extend the knockoff idea to the high-dimensional regression models and meanwhile control the FDR.  However, the singularity of the sample covariance matrix leads to the key problem that the knockoff variable cannot be directly constructed, and thus the knockoff filter also fails to control the FDR in the high-dimensional setting. To attack these problems, we propose a new proposal on knockoff filter, called as graphical knockoff filter, to consider the high-dimensional linear regression model with the Gaussian random design.  We can obtain the efficient estimator of the precision matrix based on the estimation theory of ultra-large Gaussian graphical models, which can help us to construct the cheap knockoff variable beautifully as a control group in the high-dimensional setting. It is important that the graphical knockoff procedure can directly be used to select the significant variable with nonzero coefficients efficiently while bounding the FDR under the help of Lasso solution. The properties of the proposed graphical knockoff procedures are investigated both theoretically and numerically. It is shown that the proposed graphical knockoff procedure asymptotically controls the FDR at the target level $q$ and has the higher statistical power. Compared to the existing methods, simulation results show that the proposed graphical knockoff procedure performs well numerically in terms of both the empirical false discovery rate (eFDR) and power of the test. A real data is analyzed to assess the performance of the proposed graphical knockoff procedure.

报告人简介：

李高荣，北京工业大学北京科学与工程计算研究院教授，博士生导师。华东师范大学和南加州大学博士后，全国工业统计学教学研究会常务理事、中国概率统计学会理事、北京应用统计学会常务理事、中国现场统计研究会高维数据统计分会理事、生存分析分会理事和副秘书长和美国数学评论评论员。多次访问香港浸会大学，新加坡南洋理工大学和香港城市大学。主要研究方向是非参数统计、高维统计、统计学习、纵向数据、测量误差数据和因果推断等。迄今为止，在Annals of Statistics, Journal of the American Statistical Association, Statistics and Computing, Statistica Sinica等杂志上发表学术论文80多篇，被SCI和SSCI收录50多篇。在科学出版社出版专著《纵向数据半参数模型》和《现代测量误差模型》，后者入选《现代数学基础丛书》系列。入选北京市属高等学校人才强教深化计划“中青年骨干人才培养计划”，北京市优秀人才培养资助计划和北京工业大学“京华人才”支持计划。主持国家自然科学基金、北京市自然科学基金和北京市教委科技计划面上项目等国家和省部级科研项目10余项。