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报告题目：High-dimensional Integrative Analysis with Homogeneity and Sparsity Recovery
主讲人：严晓东
报告摘要：
This paper studies integrative analysis of multiple units in the context of high-dimensional linear regression. We consider the case where a fraction of the covariates have different effects on the response across various units, e.g., some coefficients are the same for all the units, while others have a grouping structure. We propose a least squares approach, combined with a difference penalty term to penalize the difference between any two units' coefficients of the same covariate for identifying latent grouping structure, as well as a common sparsity penalty to detect important covariates. Without the need to know the grouping structure of every variable among the data units and the sparsity construction within the variables, the proposed double penalized procedure can automatically identify the covariates with heterogeneous effects, covariates with homogeneous effects, and recover the sparsity, the grouping structures of the heterogeneous covariates, and estimate the parameters simultaneously. We proceed the alternating direction method of multipliers algorithm (ADMM) through effectively utilizing the storage and reading of the datasets, and demonstrate convergence of the proposed procedure. We show that the proposed estimator enjoys the oracle property in recovering the underlying sparsity and homogeneity of the model. Simulation studies demonstrate the good performance of the new method with finite samples, and a real data example is provided for illustration.
报告人简介：
严晓东，山东大学经济学院副教授，硕士生导师，未来学者。于2013与2017年分别获得云南大学应用统计硕士与统计学博士学位，2010年毕业于山东财经大学（原山东经济学院）获得理学学士; 2014.10-2014.12在香港中文大学访问；2015.7-2018.4 在香港理工大学做全职助理研究员； 研究兴趣主要集中在高维数据的变量选择和特征筛选、缺失数据统计建模、贝叶斯局部影响分析、生存分析以及最近热门的子群分析、融合分析和深度学习。论文发表在诸如经济领域权威期刊《Journal of Econometrics》以及概率统计领域一流期刊 《Computational Statistics & Data Analysis》, 《Science China Mathematics》.
