报告题目：Sparse learning via a novel CHIP penalty and a fast solver
时 间：2023年11月29日（星期三）15:30
地 点：科研楼18号楼1233
主 办：数学与统计学院
参加对象：感兴趣的老师和学生
报告摘要：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 estab lish the nonasymptotic estimation error bounds for the global minimizer of the CHIP penalized high-dimensional linear regres sion. 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：刘妍岩教授，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。主要研究方向为生存分析、半参数统计推断、复杂高维数据模型结构选择以及大数据统计分析技术等。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，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、中国数学会女专家工作委员会委员,全国应用统计专业学位研究生教育指导委员会委员（2022.01-）。