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Optimal Subsampling for Large Sample Logistic Regression
Wang, HaiYing1,2; Zhu, Rong3; Ma, Ping4
AbstractFor 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.
KeywordA-optimality Logistic regression Massive data Optimal subsampling Rare event
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectStatistics & Probability
WOS IDWOS:000439978500029
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Document Type期刊论文
Corresponding AuthorWang, HaiYing
Affiliation1.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
Recommended Citation
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.
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