博雅讲座之六：Centre-augmented L2-type regularization for subgroup learning

讲座时间：2022年5月10日（周二）上午10：30-11:30

讲座专家：林华珍教授，西南财经大学

Abstract: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.

专家简介：林华珍 教授，博士生导师，西南财经大学统计研究中心主任, 教育部特聘教授，国家杰出青年科学基金获得者，国家百千万人才工程获得者，享受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、潜变量分析等，发表学术论文40余篇，包括发表在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。先后六次主持国家自然科学基金项目。林华珍教授是中国现场统计研究会数据科学与人工智能分会理事长，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。先后是国际统计学期刊《Biometrics》、《Scandinavian Journal of Statistics》、《Journal of Business & Economic Statistics》等期刊的Associate Editor， 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。