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Inversion-free subsampling Newton’s method for large sample logistic regression

Author

Listed:
  • J. Lars Kirkby

    (Georgia Institute of Technology)

  • Dang H. Nguyen

    (University of Alabama)

  • Duy Nguyen

    (Marist College)

  • Nhu N. Nguyen

    (University of Connecticut)

Abstract

In this paper, we develop a subsampling Newton’s method to efficiently approximate the maximum likelihood estimate in logistic regression, which is especially useful for large-sample problems. One distinct feature of our algorithm is that matrix inversion is not explicitly performed. We propose two algorithms which are used to construct iteratively a sequence of matrices which converge to the Hessian of the maximum likelihood function on the subsample. We provide numerical examples to show that the proposed method is efficient and robust.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:stpapr:v:63:y:2022:i:3:d:10.1007_s00362-021-01263-y
    DOI: 10.1007/s00362-021-01263-y
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    References listed on IDEAS

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    1. Juan Merlo & Philippe Wagner & Nermin Ghith & George Leckie, 2016. "An Original Stepwise Multilevel Logistic Regression Analysis of Discriminatory Accuracy: The Case of Neighbourhoods and Health," PLOS ONE, Public Library of Science, vol. 11(4), pages 1-31, April.
    2. Haggstrom, Gus W, 1983. "Logistic Regression and Discriminant Analysis by Ordinary Least Squares," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(3), pages 229-238, July.
    3. 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.
    4. Vivien Marx, 2013. "The big challenges of big data," Nature, Nature, vol. 498(7453), pages 255-260, June.
    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.
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    Cited by:

    1. Yan Song & Wenlin Dai, 2024. "Deterministic subsampling for logistic regression with massive data," Computational Statistics, Springer, vol. 39(2), pages 709-732, April.
    2. Huy N. Chau & J. Lars Kirkby & Dang H. Nguyen & Duy Nguyen & Nhu N. Nguyen & Thai Nguyen, 2024. "On the Inversion‐Free Newton's Method and Its Applications," International Statistical Review, International Statistical Institute, vol. 92(2), pages 284-321, August.

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