报告人：朱利平 教授 （中国人民大学）

报告题目：Penalized Interaction Estimation for Ultrahigh Dimensional Quadratic Regression

报告摘要：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，博士生导师，中国人民大学统计与大数据研究院副院长。朱利平长期从事统计学理论和方法研究，他在高维及超高维数据统计分析、半参数回归模型统计推断等领域做出了一些比较重要的研究工作，已经在统计学领域主要的四个杂志上发表论文18篇，得到了诸多著名统计学家的关注与高度评价。朱利平教授曾是《The Annals of Statistics》，《Statistica Sinica》等国际重要学术期刊的Associate Editor。目前是《Journal of Multivariate Analysis》，《Statistics and Its Interface》, 《Statistical Analysis and Data Mining》和《Journal of Systems Science and Complexity》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。

报告时间：2019年11月15日（星期五）下午3：30-5：30
报告地点：科技楼南楼702