报告人: 朱利平(中国人民大学）

日  期: 2020年1月3日

时  间: 15:30

地  点: 理科楼 LD202

摘  要: Quadratic regression goes  beyond the linear model by simultaneously including  main effects and interactions between the covariates. The problem of interaction estimation in high dimensional quadratic regression has received extensive attention in the past decade.In this article we introduce a novel method which allows us to estimate the main effects and interactions separately. Unlike existing methods for ultrahigh dimensional quadratic regressions,our proposal  does not require the widely used heredity assumption. In addition, our proposed estimates have explicit formulas  and obey the invariance principle at the population level.We estimate the interactions of matrix form under penalized convex loss function. The resulting estimates are shown to be consistent even when the covariate dimension is an exponential order of the sample size. We develop an efficient ADMM algorithm to implement the penalized estimation.  This ADMM algorithm fully explores the cheap computational cost of matrix multiplication and is much more efficient than existing penalized methods such as the all-pairs LASSO.We demonstrate the promising performance of our proposal through extensive numerical studies.

报告人简介：朱利平，中国人民大学统计与大数据研究院副院长，教授，博士生导师。2006年获得华东师范大学博士学位。入选教育部新世纪优秀人才计划以及中组部万人计划青年拔尖人才计划等，并获得国家自然科学基金委“优秀青年基金”等资助。朱利平博士一直从事复杂数据的统计理论、方法及应用研究工作，在《Journal of the Royal Statistical Society, Series B》、《The Annals of Statistics》、《Biometrika》和《Journal of the American Statistical Association》等国际顶级统计期刊发表学术论文20余篇，曾担任《The Annals of Statistics》和《Statistica Sinica》等国际重要学术期刊的Associate Editor。目前担任《Journal of Multivariate Analysis》, 《Statistics and Its Interface》等SCI期刊的Associate Editor, 《Statistics， Optimization and Computer Science》期刊统计领域Field Chief Editor，以及《系统科学与数学》和《应用概率统计》期刊编委。

学院联系人: 杨虎

欢迎广大师生积极参与！