Robust distributed multicategory angle-based classification for massive data

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...

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Bibliographic Details
Published in:Metrika Vol. 87; no. 3; pp. 299 - 323
Main Authors: Sun, Gaoming, Wang, Xiaozhou, Yan, Yibo, Zhang, Riquan
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.04.2024
Springer Nature B.V
Subjects:
Algorithms
Classification
Economic Theory/Quantitative Economics/Mathematical Methods
Euclidean space
Massive data points
Mathematics and Statistics
Parameter estimation
Probability Theory and Stochastic Processes
Random variables
Robustness
Statistics
Support vector machines
Robust distributed algorithms
Distributed setting
Weighted-based gradient estimation
MOM-based gradient estimation
Multicategory classification
ISSN:0026-1335, 1435-926X
Online Access:Get full text
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Summary: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.
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ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-023-00915-3