報(bào)告題目：Graphical Knockoff Filter for High-dimensional Regression Models
報(bào)告時(shí)間：2018年5月8日周二16:00-17:30
報(bào)告地點(diǎn)：西教五416 （理學(xué)院）
報(bào) 告 人：李高榮
報(bào)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(bào)告人簡(jiǎn)介：李高榮，北京工業(yè)大學(xué)教授，博士生導(dǎo)師，我校校友。全國(guó)工業(yè)統(tǒng)計(jì)學(xué)教學(xué)研究會(huì)常務(wù)理事、中國(guó)現(xiàn)場(chǎng)統(tǒng)計(jì)研究會(huì)高維數(shù)據(jù)統(tǒng)計(jì)分會(huì)理事、生存分析分會(huì)理事和副秘書(shū)長(zhǎng)、北京應(yīng)用統(tǒng)計(jì)學(xué)會(huì)常務(wù)理事和美國(guó)數(shù)學(xué)評(píng)論評(píng)論員。2004年7月在河北工業(yè)大學(xué)理學(xué)院獲碩士學(xué)位，2007年7月在北京工業(yè)大學(xué)應(yīng)用數(shù)理學(xué)院獲博士學(xué)位，2007年8月到2009年6月為華東師范大學(xué)金融與統(tǒng)計(jì)學(xué)院博士后，2016年3月到2017年4月為美國(guó)南加州大學(xué)Marshall商學(xué)院博士后。多次訪(fǎng)問(wèn)香港浸會(huì)大學(xué)數(shù)學(xué)系、新加坡南洋理工大學(xué)數(shù)學(xué)科學(xué)系和香港城市大學(xué)數(shù)學(xué)系。
主要研究方向是非參數(shù)統(tǒng)計(jì)、高維統(tǒng)計(jì)、模型和變量選擇、經(jīng)驗(yàn)似然、縱向數(shù)據(jù)和面板數(shù)據(jù)分析、測(cè)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(guó)內(nèi)外重要學(xué)術(shù)期刊發(fā)表學(xué)術(shù)論文80多篇，在科學(xué)出版社出版專(zhuān)著《縱向數(shù)據(jù)半?yún)?shù)模型》和《現(xiàn)代測(cè)量誤差模型》。2010年入選北京市屬高等學(xué)校人才強(qiáng)教深化計(jì)劃“中青年骨干人才培養(yǎng)計(jì)劃”和北京市優(yōu)秀人才培養(yǎng)資助計(jì)劃，2012年破格為北京工業(yè)大學(xué)“京華人才”。主持國(guó)家自然科學(xué)基金，北京市自然科學(xué)基金和北京市教育委員會(huì)科技計(jì)劃面上項(xiàng)目等10余項(xiàng)國(guó)家和省部級(jí)科研項(xiàng)目。
