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学术报告——秩:带有图形非线性仿射的大规模推断

发布者:数字与信息学院发布时间:2019-01-11浏览次数:3732

报告人:李高荣教授  北京工业大学
时间:2019年1月14日下午4点30分
地点:数学与信息学院201报告厅

摘要:

    Power and reproducibility are key to enabling refined scientific discoveries in contemporary big data applications with general high-dimensional nonlinear models. In this paper, we provide theoretical foundations on the power and robustness for the model- X knockoffs procedure introduced recently in Cand`es, Fan, Janson and Lv (2018) in high-dimensional setting when the covariate distribution is characterized by Gaussian graphical model. We establish that under mild regularity conditions, the power of the oracle knockoffs procedure with known covariate distribution in high-dimensional linear models is asymptotically one as sample size goes to infinity. When moving away from the ideal case, we suggest the modified model-X knockoffs method called graphical nonlinear knockoffs (RANK) to accommodate the unknown covariate distribution. We provide theoretical justifications on the robustness of our modified procedure by showing that the false discovery rate (FDR) is asymptotically controlled at the target level and the power is asymptotically one with the estimated covariate distribution. To the best of our knowledge, this is the first formal theoretical result on the power for the knockoffs procedure. Simulation results demonstrate that compared to existing approaches, our method performs competitively in both FDR control and power. A real data set is analyzed to further assess the performance of the suggested knockoffs 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。华东师范大学和美国南加州大学博士后,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,在统计学top期刊《Annals of Statistics》, 《Journal of the American Statistical Association》,以及一些知名的统计期刊《 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。入选北京市属高等澳门葡京赌博网站人才强教深化计划“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。


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