报告题目：Centre-augmented L2-type regularization for subgroup learning

报告时间：2022年5月20日下午 15 ：00

会议链接：https://meeting.tencent.com/dm/l6nbhVrMMpKL

会议 ID：813-604-236

主办单位：科研处/数学与统计学院

主讲人：林华珍

林华珍简介： 教授，博士生导师，西南财经大学统计研究中心主任, 国务院政府特殊津贴专家，教育部新世纪优秀人才，第十一批四川省学术和技术带头人，第十批成都市有突出贡献的优秀专家。主要研究方向为转换模型、非参数方法、生存数据分析、函数型数据分析、潜变量分析、ROC方法、偏态数据分析、捕获-再捕获数据分析。已经发表科研论文50余篇，研究成果发表在包括AoS、JASA、JoE、JRSSB、Biometrika及Biometrcs等国际统计学和计量经济学顶级期刊上论文若干。先后担任国际统计学期刊Biometrics、Scandinavian Journal of Statistics、Journal of Business & Economic Statistics、Canadian Journal of Statistics、Statistics and Its Interface、Statistical Theory and Related Fields的Associate Editor以及国内核心学术期刊《应用概率统计》、《系统科学与数学》、《数理统计与管理》编委。先后六次主持国家自然科学基金项目。林华珍教授是国际IMS-China、IBS-CHINA及ICSA-China委员，第九届全国工业统计学教学研究会副会长，中国现场统计研究会环境与资源分会、高维数据分析分会、生物医学统计学会、生存分析分会等多个分会的副理事长。

摘要：The existing methods for subgroup analysis can be roughly divided into two categories: finite mixture models (FMM) and regularization methods with an L1 -type penalty. In this paper, by introducing the group centres and L2 -type penalty in the loss function, we propose a novel centre-augmented regularization (CAR) method; this method can be regarded as a unification of the regularization method and FMM and hence exhibits higher efficiency and robustness and simpler computations than the existing methods. Particularly, its computational complexity is reduced from the $O(n^2)$ of the conventional pairwise-penalty method to only $O(nK)$, where n is the sample size and K is the number of subgroups. The asymptotic normality of CAR is established, and the convergence of the algorithm is proven. CAR is applied to a dataset from a multicenter clinical trial: Buprenorphine in the Treatment of Opiate Dependence; a larger $R^2$ is produced and three additional significant variables are identified compared to those of the existing methods.