Optimal Subsampling for Large Sample Logistic Regression

doi:10.1080/01621459.2017.1292914

CSpace > 系统科学研究所

	Optimal Subsampling for Large Sample Logistic Regression
	Wang, HaiYing 1,2; Zhu, Rong3 ; Ma, Ping 4
	2018
发表期刊	JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN	0162-1459
卷号	113 期号:522 页码:829-844
摘要	For massive data, the family of subsampling algorithms is popular to downsize the data volume and reduce computational burden. Existing studies focus on approximating the ordinary least-square estimate in linear regression, where statistical leverage scores are often used to define subsampling probabilities. In this article, we propose fast subsampling algorithms to efficiently approximate the maximum likelihood estimate in logistic regression. We first establish consistency and asymptotic normality of the estimator from a general subsampling algorithm, and then derive optimal subsampling probabilities that minimize the asymptotic mean squared error of the resultant estimator. An alternative minimization criterion is also proposed to further reduce the computational cost. The optimal subsampling probabilities depend on the full data estimate, so we develop a two-step algorithm to approximate the optimal subsampling procedure. This algorithm is computationally efficient and has a significant reduction in computing time compared to the full data approach. Consistency and asymptotic normality of the estimator from a two-step algorithm are also established. Synthetic and real datasets are used to evaluate the practical performance of the proposed method. Supplementary materials for this article are available online.
关键词	A-optimality Logistic regression Massive data Optimal subsampling Rare event
DOI	10.1080/01621459.2017.1292914
语种	英语
资助项目	National Natural Science Foundation of China[11301514] ; National Natural Science Foundation of China[71532013] ; National Science Foundation[DMS-1440037(1222718)] ; National Science Foundation[DMS-1438957(1055815)] ; National Science Foundation[DMS-1440038(1228288)] ; National Institutes of Health[R01GM113242] ; National Institutes of Health[R01GM122080] ; Microsoft Azure ; Simons Foundation Collaboration Grant for Mathematicians[515599]
WOS研究方向	Mathematics
WOS类目	Statistics & Probability
WOS记录号	WOS:000439978500029
出版者	AMER STATISTICAL ASSOC
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/30837
专题	系统科学研究所
通讯作者	Wang, HaiYing
作者单位	1.Univ New Hampshire, Dept Math & Stat, Durham, NH 03824 USA 2.Univ Connecticut, Dept Stat, Storrs, CT 06269 USA 3.Chinese Acad Sci, Acad Math & Syst Sci, Beijing, Peoples R China 4.Univ Georgia, Dept Stat, Athens, GA 30602 USA
推荐引用方式 GB/T 7714	Wang, HaiYing,Zhu, Rong,Ma, Ping. Optimal Subsampling for Large Sample Logistic Regression[J]. JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,2018,113(522):829-844.
APA	Wang, HaiYing,Zhu, Rong,&Ma, Ping.(2018).Optimal Subsampling for Large Sample Logistic Regression.JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION,113(522),829-844.
MLA	Wang, HaiYing,et al."Optimal Subsampling for Large Sample Logistic Regression".JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 113.522(2018):829-844.