报告简介  Abstract

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.

This is a joint work with Prof. Binyan Jiang and Prof. Liping Zhu.

嘉宾简介  About the Speaker

王成博士，2013年博士毕业于中国科学技术大学，曾获得过中科院院长特别奖，2014年9月加入上海交通大学数学科学学院担任特别研究员。主要研究方向为随机矩阵理论及高维协方差矩阵的统计推断等。在统计领域核心期刊Statistica Sinica, Electronic Journal of Statistics等杂志上发表学术论文十余篇。主持国家自然科学基金青年基金，上海市青年科技英才扬帆计划以及企业项目三项，参与国家自然科学基金重点项目、面上项目等多项。

讲座海报Poster