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Deterministic subsampling for logistic regression with massive data

Author

Listed:
  • Yan Song

    (Renmin University of China)

  • Wenlin Dai

    (Renmin University of China)

Abstract

For logistic regression with massive data, subsampling is an effective way to alleviate the computational challenge. In contrast to most existing methods in the literature that select subsamples randomly, we propose to obtain subsamples in a deterministic way. To be more specific, we measure with leverage scores the influence of each sample to model fitting and select the ones with the highest scores deterministically. We propose a faster alternative method by mimicking the leverage scores with a simple and intuitive form. Our methods pick subsamples catering for constructing a linear classification boundary and hence are more efficient when the subsample size is small. We derive non-asymptotic properties of the two methods regarding the observed information, prediction, and parameter estimation accuracy. Extensive simulation studies and two real applications validate the theoretical results and demonstrate the superiority of our methods.

Suggested Citation

  • Yan Song & Wenlin Dai, 2024. "Deterministic subsampling for logistic regression with massive data," Computational Statistics, Springer, vol. 39(2), pages 709-732, April.
    • Handle: RePEc:spr:compst:v:39:y:2024:i:2:d:10.1007_s00180-022-01319-z
    DOI: 10.1007/s00180-022-01319-z
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    References listed on IDEAS

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    1. J. Lars Kirkby & Dang H. Nguyen & Duy Nguyen & Nhu N. Nguyen, 2022. "Inversion-free subsampling Newton’s method for large sample logistic regression," Statistical Papers, Springer, vol. 63(3), pages 943-963, June.
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    5. Yaqiong Yao & HaiYing Wang, 2019. "Optimal subsampling for softmax regression," Statistical Papers, Springer, vol. 60(2), pages 585-599, April.
    6. 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.
    Full references (including those not matched with items on IDEAS)

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