報告題目：Graphical Knockoff Filter for High-dimensional Regression Models
報告時間：2018年5月8日周二16:00-17:30
報告地點：西教五416 （理學院）
報 告 人：李高榮
報告摘要：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.
報告人簡介：李高榮，北京工業大學教授，博士生導師，我校校友。全國工業統計學教學研究會常務理事、中國現場統計研究會高維數據統計分會理事、生存分析分會理事和副秘書長、北京應用統計學會常務理事和美國數學評論評論員。2004年7月在河北工業大學理學院獲碩士學位，2007年7月在北京工業大學應用數理學院獲博士學位，2007年8月到2009年6月為華東師范大學金融與統計學院博士后，2016年3月到2017年4月為美國南加州大學Marshall商學院博士后。多次訪問香港浸會大學數學系、新加坡南洋理工大學數學科學系和香港城市大學數學系。
主要研究方向是非參數統計、高維統計、模型和變量選擇、經驗似然、縱向數據和面板數據分析、測量誤差等。迄今為止，在《The Annals of Statistics》、《Statistics and Computing》、《StatisticaSinica》、《Journal of Multivariate Analysis》、《Journal of Computational Biology》和《Computational Statistics and Data Analysis》等國內外重要學術期刊發表學術論文80多篇，在科學出版社出版專著《縱向數據半參數模型》和《現代測量誤差模型》。2010年入選北京市屬高等學校人才強教深化計劃“中青年骨干人才培養計劃”和北京市優秀人才培養資助計劃，2012年破格為北京工業大學“京華人才”。主持國家自然科學基金，北京市自然科學基金和北京市教育委員會科技計劃面上項目等10余項國家和省部級科研項目。
