报告题目：On a class of high dimensional linear regression methods with debiasing and thresholding

报告摘要： In this talk, inspired by classical regularization theory, we introduce a unified framework for designing and analyzing a broad class of linear regression approaches. Our framework encompasses traditional methods like least squares regression and Ridge regression, as well as innovative techniques, including seven novel regression methods such as Landweber and Showalter regressions. Within this framework, we further propose a class of debiased and thresholded regression methods to promote feature selection, particularly in terms of sparsity. These methods may offer advantages over conventional regression methods, including Lasso, as they can be easily computed using a closed-form expression. Theoretically, we prove consistency results and Gaussian approximation theorems for this new class of regularization methods. Extensive numerical simulations further demonstrate that debiased and thresholded counterparts of linear regression methods exhibit favorable finite sample performance and may be preferable in certain settings.

报告时间：8月4日 15：00-16：00，地点：理学楼609

专家简介：深圳北理莫斯科大学和北京理工大学双聘教授、博士生导师，莫大-北理-深北莫应用数学联合研究中心执行主任、深圳北理莫斯科大学计算数学与控制系中方负责人。深圳市数学学会副理事长、“深圳杯”数学建模挑战赛专家委员会委员、中国工业与应用数学学会反问题与成像专业委员会理事、中国运筹学会数学与智能分会理事。2022年世界数学家大会Kovalevskaya奖获得者、国家高层次青年人才计划获得者(2019)、德国洪堡学者(2017)、深圳市特殊津贴(2022)、深圳市杰青项目(2024)。2014年获得莫斯科国立大学数学物理副博士。主要研究领域是数学物理反问题的数学建模、数学理论和科学计算。在应用数学和统计学的国际顶级杂志发表高水平论文50多篇。目前主持国家重点研发青年科学家项目、北京市重点项目、国家自然科学基金面上项目、广东省和深圳市等多项省部级项目。