学术报告：From Penalization to Over-parameterization: Achieving Implicit Regularization for High-dimensional Linear Errors-in-Variables Models

报告时间：12月31日（星期三）上午10:00-12:00

报告地点：沙河校区，学院1号楼102会议室

主持人：盖玉洁教授

报告人：李高荣，北京师范大学，教授

报告摘要：Regularization methods are crucial for the analysis of high-dimensional data, with most methods adding a penalty term to the loss function explicitly. In this paper, we introduce an implicit regularization technique through over-parameterization and propose a calibrated penalty-free (CPF) estimation method for high-dimensional linear errors-in-variables models. This method calibrates the bias caused by measurement errors while avoiding the bias introduced by penalty terms. We use the gradient descent algorithm to minimize the over-parameterized calibrated loss function without penalties, resulting in a sparse estimate of regression coefficients and thus achieving implicit regularization. Furthermore, a novel bootstrap methodology is introduced to address the challenge posed by the unknown covariance matrix of measurement errors. The oracle inequality for estimation error is established under certain regularity conditions. Extensive simulation studies and a real data analysis illustrate the competitive finite sample performance of the proposed method.

报告人简介：李高荣，北京师范大学统计学院教授，博士生导师，北京师范大学第十二届“最受本科生欢迎的十佳教师”。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Annals of Statistics, Journal of the American Statistical Association, Journal of Business & Economic Statistics, Statistics and Computing,《中国科学：数学》和《统计研究》等学术期刊上发表学术论文120余篇。出版4部著作：《纵向数据半参数模型》、《现代测量误差模型》(入选“现代数学基础丛书”系列)、《多元统计分析》(入选“统计与数据科学丛书”系列，2023年荣获北京高校优质本科教材）和统计学习（R语言版）。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多项。

撰稿人：刘洁

审稿人：邓露