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

报告时间：2018年5月8日周二16:00-17:30

报告地点：西教五416 （理学院）

报 告 人：李高荣

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，北京工业大学教授，博士生导师，我司校友。全国工业统计学教学研究会常务理事、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、北京应用统计学会常务理事和美国数学评论评论员。2004年7月在williamhill中文欢迎您理学院获硕士学位，2007年7月在北京工业大学应用数理学院获博士学位，2007年8月到2009年6月为华东师范大学金融与统计学院博士后，2016年3月到2017年4月为美国南加州大学Marshall商学院博士后。多次访问香港浸会大学数学系、新加坡南洋理威廉希尔中文官方网站学数学科学系和香港城市大学数学系。

主要研究方向是非参数统计、高维统计、模型和变量选择、经验似然、纵向数据和面板数据分析、测量误差等。迄今为止，在《The Annals of Statistics》、《Statistics and Computing》、《StatisticaSinica》、《Journal of Multivariate Analysis》、《Journal of Computational Biology》和《Computational Statistics and Data Analysis》等国内外重要学术期刊发表学术论文80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》。2010年入选北京市属高等公司人才强教深化计划“中青年骨干人才培养计划”和北京市优秀人才培养资助计划，2012年破格为北京工业大学“京华人才”。主持国家自然科学基金，北京市自然科学基金和北京市教育委员会科技计划面上项目等10余项国家和省部级科研项目。