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

报 告 人：李高荣教授 博士生导师

报告时间：2017年10月26日（周四）下午3:00

报告地点：数学与统计学院310报告厅

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。主要研究方向是复杂高维数据分析、深度学习、模型和变量选择、非参数统计、经验似然、纵向数据和测量误差模型等。于2007年7月在北京工业大学应用数理学院获得概率论与数理统计专业博士学位，2007年8月到2009年6月在华东师范大学金融与统计学院从事博士后研究工作，2016年3月到2017年3月为美国南加州大学Marshall商学院博士后。迄今为止，在《The Annals of Statistics》、《Statistics and Computing》、《Journal of Multivariate Analysis》、《Statistica Sinica》和《Computational Statistics and Data Analysis》等国内外重要学术期刊发表学术论文70多篇，其中40多篇发表在国际SCI期刊，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》。

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