IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v63y2022i3d10.1007_s00362-021-01263-y.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-021-01263-y
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00362-021-01263-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. Yaqiong Yao & HaiYing Wang, 2019. "Optimal subsampling for softmax regression," Statistical Papers, Springer, vol. 60(2), pages 585-599, April.
    3. 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.
    4. Vivien Marx, 2013. "The big challenges of big data," Nature, Nature, vol. 498(7453), pages 255-260, June.
    5. 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.
    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Su, Miaomiao & Wang, Ruoyu & Wang, Qihua, 2022. "A two-stage optimal subsampling estimation for missing data problems with large-scale data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    2. Jun Yu & HaiYing Wang, 2022. "Subdata selection algorithm for linear model discrimination," Statistical Papers, Springer, vol. 63(6), pages 1883-1906, December.
    3. Ziyang Wang & HaiYing Wang & Nalini Ravishanker, 2023. "Subsampling in Longitudinal Models," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-29, March.
    4. Amalan Mahendran & Helen Thompson & James M. McGree, 2023. "A model robust subsampling approach for Generalised Linear Models in big data settings," Statistical Papers, Springer, vol. 64(4), pages 1137-1157, August.
    5. Yuxin Sun & Wenjun Liu & Ye Tian, 2024. "Projection-Uniform Subsampling Methods for Big Data," Mathematics, MDPI, vol. 12(19), pages 1-16, September.
    6. Xiaohui Yuan & Yong Li & Xiaogang Dong & Tianqing Liu, 2022. "Optimal subsampling for composite quantile regression in big data," Statistical Papers, Springer, vol. 63(5), pages 1649-1676, October.
    7. Feifei Wang & Danyang Huang & Tianchen Gao & Shuyuan Wu & Hansheng Wang, 2022. "Sequential one‐step estimator by sub‐sampling for customer churn analysis with massive data sets," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1753-1786, November.
    8. Jun Yu & Jiaqi Liu & HaiYing Wang, 2023. "Information-based optimal subdata selection for non-linear models," Statistical Papers, Springer, vol. 64(4), pages 1069-1093, August.
    9. Duarte, Belmiro P.M. & Atkinson, Anthony C. & Oliveira, Nuno M.C., 2024. "Using hierarchical information-theoretic criteria to optimize subsampling of extensive datasets," LSE Research Online Documents on Economics 121641, London School of Economics and Political Science, LSE Library.
    10. 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.
    11. Deng, Jiayi & Huang, Danyang & Ding, Yi & Zhu, Yingqiu & Jing, Bingyi & Zhang, Bo, 2024. "Subsampling spectral clustering for stochastic block models in large-scale networks," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    12. Zhang, Haixiang & Wang, HaiYing, 2021. "Distributed subdata selection for big data via sampling-based approach," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    13. Hector, Emily C. & Luo, Lan & Song, Peter X.-K., 2023. "Parallel-and-stream accelerator for computationally fast supervised learning," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    14. Sokbae Lee & Serena Ng, 2020. "An Econometric Perspective on Algorithmic Subsampling," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 45-80, August.
    15. Lee, JooChul & Wang, HaiYing & Schifano, Elizabeth D., 2020. "Online updating method to correct for measurement error in big data streams," Computational Statistics & Data Analysis, Elsevier, vol. 149(C).
    16. 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.
    17. Lin Zhu & Xiantao Liu & Sha He & Jun Shi & Ming Pang, 2015. "Keywords co-occurrence mapping knowledge domain research base on the theory of Big Data in oil and gas industry," Scientometrics, Springer;Akadémiai Kiadó, vol. 105(1), pages 249-260, October.
    18. Zhang, Yi & Huang, Ying & Porter, Alan L. & Zhang, Guangquan & Lu, Jie, 2019. "Discovering and forecasting interactions in big data research: A learning-enhanced bibliometric study," Technological Forecasting and Social Change, Elsevier, vol. 146(C), pages 795-807.
    19. Bolte, Gabriele, 2018. "Epidemiologische Methoden und Erkenntnisse als eine Grundlage für Stadtplanung und gesundheitsfördernde Stadtentwicklung," Forschungsberichte der ARL: Aufsätze, in: Baumgart, Sabine & Köckler, Heike & Ritzinger, Anne & Rüdiger, Andrea (ed.), Planung für gesundheitsfördernde Städte, volume 8, pages 118-134, ARL – Akademie für Raumentwicklung in der Leibniz-Gemeinschaft.
    20. Stefano Bianchini & Moritz Müller & Pierre Pelletier, 2022. "Artificial intelligence in science: An emerging general method of invention," Post-Print hal-03958025, HAL.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:stpapr:v:63:y:2022:i:3:d:10.1007_s00362-021-01263-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.