报告题目：Newton–Raphson Meets Sparsity: Sparse Learning via a Novel Penalty and a Fast Solver
报告人：刘妍岩教授
单位：武汉大学数学与统计学院
时间：2025年11月6日 8:00-12:00
地点：线上腾讯会议：231 126 383；线下数信学院305
摘要：
In machine learning and statistics, the penalized regression methods are the main tools for variable selection (or feature selection) in high-dimensional sparse data analysis. Due to the nonsmoothness of the associated thresholding operators of commonly used penalties such as the least absolute shrinkage and selection operator (LASSO), the smoothly clipped absolute deviation (SCAD), and the minimax concave penalty (MCP), the classical Newton–Raphson algorithm cannot be used. In this article, we propose a cubic Hermite interpolation penalty (CHIP) with a smoothing thresholding operator. Theoretically, we establish the nonasymptotic estimation error bounds for the global minimizer of the CHIP penalized high-dimensional linear regression. Moreover, we show that the estimated support coincides with the target support with a high probability.We derive the Karush–Kuhn–Tucker (KKT) condition for the CHIP penalized estimator and then develop a support detection-based Newton–Raphson (SDNR) algorithm to solve it. Simulation studies demonstrate that the proposed method performs well in a wide range of finite sample situations.We also illustrate the application of our method with a real data example.
报告人简介：
刘妍岩，武汉大学数学与统计学院教授，博士生导师。2001年获武汉大学理学博士学位。主要研究方向为删失数据半参数统计推断、复杂高维数据模型结构选择以及大数据分布式计算等。曾到美国北卡来罗纳大学教堂山分校、加拿大Simon-Fraser大学、香港理工大学、香港中文大学、德国Greifswald大学等学校短期访问和工作。主持完成国家自然科学基金以及教育部基金项目6项，在统计学期刊 Journal of Machine Learning Research, Biometrics, Biostatistics, Genetics，Lifetime Data Analysis等期刊发表SCI研究论文六十余篇。目前担任国际统计学期刊statistical papers 副主编（2020-），数理统计与管理副主编（2022.01-2025.12）,中国现场统计学会第十一届理事会常务理事（2020-）、中国数学会女专家工作委员会委员（2021-）,全国应用统计专业学位研究生教育指导委员会委员（2022.01-）。
