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Optimal subsample selection for massive logistic regression with distributed data

Author

Listed:
  • Lulu Zuo

    (Tianjin University)

  • Haixiang Zhang

    (Tianjin University)

  • HaiYing Wang

    (University of Connecticut)

  • Liuquan Sun

    (Chinese Academy of Sciences)

Abstract

With the emergence of big data, it is increasingly common that the data are distributed. i.e., the data are stored at many distributed sites (machines or nodes) owing to data collection or business operations, etc. We propose a distributed subsampling procedure in such a setting to efficiently approximate the maximum likelihood estimator for the logistic regression. We establish the consistency and asymptotic normality of the subsample estimator given the full data. The optimal subsampling probabilities and optimal allocation sizes are explicitly obtained. We develop a two-step algorithm to approximate the optimal subsampling procedure. Numerical simulations and an application to airline data are presented to evaluate the performance of our subsampling method.

Suggested Citation

  • Lulu Zuo & Haixiang Zhang & HaiYing Wang & Liuquan Sun, 2021. "Optimal subsample selection for massive logistic regression with distributed data," Computational Statistics, Springer, vol. 36(4), pages 2535-2562, December.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:4:d:10.1007_s00180-021-01089-0
    DOI: 10.1007/s00180-021-01089-0
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    References listed on IDEAS

    as
    1. HaiYing Wang & Min Yang & John Stufken, 2019. "Information-Based Optimal Subdata Selection for Big Data Linear Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 393-405, January.
    2. Michael I. Jordan & Jason D. Lee & Yun Yang, 2019. "Communication-Efficient Distributed Statistical Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 668-681, April.
    3. Shi, Chengchun & Lu, Wenbin & Song, Rui, 2018. "A massive data framework for M-estimators with cubic-rate," LSE Research Online Documents on Economics 102111, London School of Economics and Political Science, LSE Library.
    4. Chengchun Shi & Wenbin Lu & Rui Song, 2018. "A Massive Data Framework for M-Estimators with Cubic-Rate," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1698-1709, October.
    5. HaiYing Wang & Rong Zhu & Ping Ma, 2018. "Optimal Subsampling for Large Sample Logistic Regression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(522), pages 829-844, April.
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    Cited by:

    1. Tianzhen Wang & Haixiang Zhang, 2022. "Optimal subsampling for multiplicative regression with massive data," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 76(4), pages 418-449, November.

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