Optimal Subsampling for Large Sample Logistic Regression

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 proba...

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Bibliographic Details
Published in:Journal of the American Statistical Association Vol. 113; no. 522; pp. 829 - 844
Main Authors: Wang, HaiYing, Zhu, Rong, Ma, Ping
Format: Journal Article
Language:English
Published: United States Taylor & Francis 03.04.2018
Taylor & Francis Group,LLC
Taylor & Francis Ltd
Subjects:
A-optimality
Algorithms
Asymptotic properties
Computational efficiency
Computing costs
Computing time
Consistency
Data
data collection
equations
Logistic regression
Massive data
Maximum likelihood estimates
Minimization
Normality
Optimal subsampling
Optimization
Probability
Rare event
Regression
Regression analysis
Statistical analysis
Statistical methods
Statistics
Theory and Methods
Rare Event
Logistic Regression
Optimal Subsampling
A-optimality
Massive Data
ISSN:0162-1459, 1537-274X, 1537-274X
Online Access:Get full text
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Summary: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.
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HaiYing Wang and Rong Zhu contribute equally.
ISSN:0162-1459
1537-274X
1537-274X
DOI:10.1080/01621459.2017.1292914