Byzantine-tolerant distributed learning of finite mixture models under partial corruptions
Abstract
Finite mixture models characterize heterogeneous populations and are increasingly fitted to distributed data using split-and-conquer procedures that aggregate local mixture estimates at a central server. The aggregation step can be seriously compromised when transmitted local mixture estimates are partially or completely corrupted. To guard against Byzantine failures, existing robust aggregation methods have been developed for settings in which a local mixture estimate is either entirely authentic or entirely corrupted. Such methods can discard useful information when only some component estimates are corrupted. We consider component-wise Byzantine failure, in which some component estimates may be corrupted, but for each mixture component, a majority of the corresponding local estimates remain authentic. We propose component-wise filtered mixture reduction (CFMR), which selects a data-driven anchor, aligns transmitted components, filters each aligned cluster by a majority radius, and aggregates the retained estimates through mixture reduction. By filtering out only unreliable components, CFMR preserves authentic information from partially corrupted machines without requiring knowledge of the failure rates. We establish an adaptive convergence bound for CFMR and show that, under suitable conditions, it attains the oracle rate that would be achieved if the authentic component estimates were known in advance. Simulations and a real-data application show that CFMR remains close to the component-level oracle, whereas whole-machine filtering and unprotected aggregation can deteriorate substantially.
Related
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BibTeX
@misc{zhang2026byzantinetolerant,
title = {{Byzantine-tolerant distributed learning of finite mixture models under partial corruptions}},
author = {Yimei Zhang and Jiahua Chen and Xiaozhou Wang and Yan Shuo Tan and Qiong Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11309},
eprint = {2609.11309},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11309},
}
RIS
TY - UNPB
TI - Byzantine-tolerant distributed learning of finite mixture models under partial corruptions
AU - Yimei Zhang
AU - Jiahua Chen
AU - Xiaozhou Wang
AU - Yan Shuo Tan
AU - Qiong Zhang
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11309
UR - https://arxiv.org/abs/2609.11309
AB - Finite mixture models characterize heterogeneous populations and are increasingly fitted to distributed data using split-and-conquer procedures that aggregate local mixture estimates at a central server. The aggregation step can be seriously compromised when transmitted local mixture estimates are partially or completely corrupted. To guard against Byzantine failures, existing robust aggregation methods have been developed for settings in which a local mixture estimate is either entirely authentic or entirely corrupted. Such methods can discard useful information when only some component estimates are corrupted. We consider component-wise Byzantine failure, in which some component estimates may be corrupted, but for each mixture component, a majority of the corresponding local estimates remain authentic. We propose component-wise filtered mixture reduction (CFMR), which selects a data-driven anchor, aligns transmitted components, filters each aligned cluster by a majority radius, and aggregates the retained estimates through mixture reduction. By filtering out only unreliable components, CFMR preserves authentic information from partially corrupted machines without requiring knowledge of the failure rates. We establish an adaptive convergence bound for CFMR and show that, under suitable conditions, it attains the oracle rate that would be achieved if the authentic component estimates were known in advance. Simulations and a real-data application show that CFMR remains close to the component-level oracle, whereas whole-machine filtering and unprotected aggregation can deteriorate substantially.
ER -