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Robust distributed multicategory angle-based classification for massive data

Author

Listed:
  • Gaoming Sun

    (East China Normal University)

  • Xiaozhou Wang

    (East China Normal University
    East China Normal University)

  • Yibo Yan

    (East China Normal University)

  • Riquan Zhang

    (Shanghai University of International Business and Economics)

Abstract

Multicategory classification problems are frequently encountered in practice. Considering that the massive data sets are increasingly common and often stored locally, we first provide a distributed estimation in the multicategory angle-based classification framework and obtain its excess risk under general conditions. Further, under varied robustness settings, we develop two robust distributed algorithms to provide robust estimations of the multicategory classification. The first robust distributed algorithm takes advantage of median-of-means (MOM) and is designed by the MOM-based gradient estimation. The second robust distributed algorithm is implemented by constructing the weighted-based gradient estimation. The theoretical guarantees of our algorithms are established via the non-asymptotic error bounds of the iterative estimations. Some numerical simulations demonstrate that our methods can effectively reduce the impact of outliers.

Suggested Citation

  • Gaoming Sun & Xiaozhou Wang & Yibo Yan & Riquan Zhang, 2024. "Robust distributed multicategory angle-based classification for massive data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 87(3), pages 299-323, April.
    • Handle: RePEc:spr:metrik:v:87:y:2024:i:3:d:10.1007_s00184-023-00915-3
    DOI: 10.1007/s00184-023-00915-3
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    References listed on IDEAS

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    1. Chong Zhang & Yufeng Liu, 2014. "Multicategory angle-based large-margin classification," Biometrika, Biometrika Trust, vol. 101(3), pages 625-640.
    2. Luo, Jiyu & Sun, Qiang & Zhou, Wen-Xin, 2022. "Distributed adaptive Huber regression," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    3. Lee, Yoonkyung & Lin, Yi & Wahba, Grace, 2004. "Multicategory Support Vector Machines: Theory and Application to the Classification of Microarray Data and Satellite Radiance Data," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 67-81, January.
    4. Yang, Yi & Guo, Yuxuan & Chang, Xiangyu, 2021. "Angle-based cost-sensitive multicategory classification," Computational Statistics & Data Analysis, Elsevier, vol. 156(C).
    5. Michael I. Jordan & Jason D. Lee & Yun Yang, 2019. "Communication-Efficient Distributed Statistical Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 668-681, April.
    6. Adarsh Prasad & Arun Sai Suggala & Sivaraman Balakrishnan & Pradeep Ravikumar, 2020. "Robust estimation via robust gradient estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(3), pages 601-627, July.
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