IDEAS home Printed from https://ideas.repec.org/a/eee/ecosta/v29y2024icp224-237.html
   My bibliography  Save this article

Fast Optimal Subsampling Probability Approximation for Generalized Linear Models

Author

Listed:
  • Lee, JooChul
  • Schifano, Elizabeth D.
  • Wang, HaiYing

Abstract

For massive data, subsampling techniques are popular to mitigate computational burden by reducing the data size. In a subsampling approach, subsampling probabilities for each data point are specified to obtain an informative sub-data, and then estimates based on the sub-data are obtained to approximate estimates from the full data. Assigning subsampling probabilities based on minimization of the asymptotic mean squared error of the estimator from a general subsample (A-optimality criterion) is a popular approach, however, it is still computationally demanding to calculate the probabilities under this setting. To efficiently approximate the A-optimal subsampling probabilities for generalized linear models, randomized algorithms are proposed. To develop the algorithms, the Johnson-Lindenstrauss Transform and Subsampled Randomized Hadamard Transform are used. Additionally, optimal subsampling probabilities are derived for the Gaussian linear model in the case where both the regression coefficients and dispersion parameter are of interest, and algorithms are developed to approximate the optimal subsampling probabilities. Simulation studies indicate that the estimators based on the developed algorithms have excellent performance for statistical inference and have substantial savings in computing time compared to the direct calculation of the A-optimal subsampling probabilities.

Suggested Citation

  • Lee, JooChul & Schifano, Elizabeth D. & Wang, HaiYing, 2024. "Fast Optimal Subsampling Probability Approximation for Generalized Linear Models," Econometrics and Statistics, Elsevier, vol. 29(C), pages 224-237.
    • Handle: RePEc:eee:ecosta:v:29:y:2024:i:c:p:224-237
    DOI: 10.1016/j.ecosta.2021.02.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S2452306221000290
    Download Restriction: Full text for ScienceDirect subscribers only. Contains open access articles
    File URL: https://libkey.io/10.1016/j.ecosta.2021.02.007?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. 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).
    2. 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.
    3. Yishu Xue & HaiYing Wang & Jun Yan & Elizabeth D. Schifano, 2020. "An online updating approach for testing the proportional hazards assumption with streams of survival data," Biometrics, The International Biometric Society, vol. 76(1), pages 171-182, March.
    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. 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.
    2. 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).
    3. 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.
    4. 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).
    5. 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.
    6. Jun Yu & HaiYing Wang, 2022. "Subdata selection algorithm for linear model discrimination," Statistical Papers, Springer, vol. 63(6), pages 1883-1906, December.
    7. 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.
    8. Ping Wang & Lu Lin, 2023. "Conditional characteristic feature screening for massive imbalanced data," Statistical Papers, Springer, vol. 64(3), pages 807-834, June.
    9. 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.
    10. 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.
    11. 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.
    12. Tao Zou & Xian Li & Xuan Liang & Hansheng Wang, 2021. "On the Subbagging Estimation for Massive Data," Papers 2103.00631, arXiv.org.
    13. 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).
    14. Zhang, Haixiang & Wang, HaiYing, 2021. "Distributed subdata selection for big data via sampling-based approach," Computational Statistics & Data Analysis, Elsevier, vol. 153(C).
    15. 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).
    16. Sokbae Lee & Serena Ng, 2020. "An Econometric Perspective on Algorithmic Subsampling," Annual Review of Economics, Annual Reviews, vol. 12(1), pages 45-80, August.
    17. Yujing Shao & Lei Wang, 2022. "Optimal subsampling for composite quantile regression model in massive data," Statistical Papers, Springer, vol. 63(4), pages 1139-1161, August.
    18. Xuejun Ma & Shaochen Wang & Wang Zhou, 2022. "Statistical inference in massive datasets by empirical likelihood," Computational Statistics, Springer, vol. 37(3), pages 1143-1164, July.
    19. 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.
    20. Seong‐H. Lee & Yanyuan Ma & Ying Wei & Jinbo Chen, 2023. "Optimal sampling for positive only electronic health record data," Biometrics, The International Biometric Society, vol. 79(4), pages 2974-2986, December.

    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:eee:ecosta:v:29:y:2024:i:c:p:224-237. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/econometrics-and-statistics .

    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.