Optimal Subsampling for Model Robustness in Big Data

艾明要，北京大学数学科学学院二级教授，北京大学教材建设博雅特聘教授。全国应用统计专业学位研究生教育指导委员会委员、培养组组长，中国现场统计研究会第十一届副理事长，中国概率统计学会第十一届秘书长，中国统计学会常务理事。全国统计教材编审委员会专业委员，科学出版社《统计与数据科学丛书》编委，国际重要SCI期刊Stat Sinica、JSPI、SPL和Stat编委，国内核心期刊 《系统科学与数学》《数理统计与管理》《数学进展》编委。主要从事大数据采样理论与算法、试验设计与分析、应用统计的教学和研究工作，在AOS、JASA、Biometrika、《中国科学》等国内外重要期刊发表学术论文80余篇。主持国家自然科学基金重点项目1项、国际合作研究项目1项、重点项目子课题1项、面上项目5项，参与国家自然科学基金重大项目1项、科技部重点研发计划项目2项。两次获得北京大学优秀博士学位论文指导教师，获北京大学优秀教学成果一等奖、北京市高等学校优秀教学成果二等奖。

Subsampling is an effective approach to address computational challenges associated with massive datasets. However, existing subsampling methods do not consider model uncertainty. In this talk, we first review optimal subsampling techniques from linear model, to generalized linear model, and to estimation equations, then investigate the subsampling technique for the Akaike information criterion (AIC) and extend the subsampling method to the smoothed AIC model-averaging framework in the context of generalized linear models. By correcting the asymptotic bias of the maximized subsample objective function used to approximate the Kullback-Leibler divergence, we derive the form of the AIC based on the subsample and provide a subsampling strategy for the smoothed AIC model-averaging estimator. The corresponding asymptotic properties of the loss and the resulting estimator is also studied. A practically implementable algorithm is developed, and its performance is evaluated through numerical experiments on both real and simulated datasets.