报告人：王成
报告地点：腾讯会议（会议ID：139223918 会议密码：200804）
报告时间：2020年08月04日星期二14:00-15:00
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 all pairs LASSO. We demonstrate the promising performance of our proposal through extensive numerical studies.
主讲人简介：
王 成，上海交通大学数学科学学院特别研究员。2013年博士毕业于中国科学技术大学，主要研究方向为随机矩阵理论和高维数据的统计推断等，在统计领域核心期刊上发表学术论文10余篇。 科研项目得到上海市青年科技英才“扬帆计划”项目及国家自然科学青年基金支持。
