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Optimal subsampling for softmax regression

Author

Listed:
  • Yaqiong Yao

    (University of Connecticut)

  • HaiYing Wang

    (University of Connecticut)

Abstract

To meet the challenge of massive data, Wang et al. (J Am Stat Assoc 113(522):829–844, 2018b) developed an optimal subsampling method for logistic regression. The purpose of this paper is to extend their method to softmax regression, which is also called multinomial logistic regression and is commonly used to model data with multiple categorical responses. We first derive the asymptotic distribution of the general subsampling estimator, and then derive optimal subsampling probabilities under the A-optimality criterion and the L-optimality criterion with a specific L matrix. Since the optimal subsampling probabilities depend on the unknowns, we adopt a two-stage adaptive procedure to address this issue and use numerical simulations to demonstrate its performance.

Suggested Citation

  • Yaqiong Yao & HaiYing Wang, 2019. "Optimal subsampling for softmax regression," Statistical Papers, Springer, vol. 60(2), pages 585-599, April.
    • Handle: RePEc:spr:stpapr:v:60:y:2019:i:2:d:10.1007_s00362-018-01068-6
    DOI: 10.1007/s00362-018-01068-6
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    Citations

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    Cited by:

    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. Jun Yu & HaiYing Wang, 2022. "Subdata selection algorithm for linear model discrimination," Statistical Papers, Springer, vol. 63(6), pages 1883-1906, December.
    3. 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.
    4. Hong Pan & Hanxun Zhou, 2020. "Study on convolutional neural network and its application in data mining and sales forecasting for E-commerce," Electronic Commerce Research, Springer, vol. 20(2), pages 297-320, June.
    5. 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.
    6. 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).
    7. 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.

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