Distributed Robust Algorithms with Dependent Sampling

Baobin Wang, Ting Hu and Liangzhen Lei ()
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Baobin Wang: Hubei Province Key Laboratory of Systems Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081, China
Ting Hu: School of Management, Xi’an Jiaotong University, Xi’an 710049, China
Liangzhen Lei: School of Mathematical Sciences, Capital Normal Univeristy, Beijing 100048, China

Mathematics, 2025, vol. 13, issue 23, 1-20

Abstract: Robust algorithms have been widely used and intensively studied in the communities of engineering, statistics, and machine learning since such algorithms are less sensitive to outliers and effective in addressing the issue of non-Gaussian noise during the learning process. In this paper we study the learning performance of a distributed robust algorithm with mixing dependent samples, where big data are collected distributively and have a dependence structure. Learning rates are derived by means of an integral operator decomposition technique and probability inequalities in Hilbert spaces. The results show that with a suitable robustification parameter, the performance of the distributed robust algorithm is comparable with that of its non-distributed counterpart, even if the dependent feature restricts the availability and the effective amount of data.

Keywords: robustness; dependent samples; distributed learning; integral operator; learning rates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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