Byzantine-tolerant distributed learning of finite mixture models under partial corruptions

2026-09-10

AI Summary

本文提出了一种组件级过滤混合缩减方法（CFMR），以解决在部分组件估计值被破坏的情况下，分布式学习有限混合模型的问题。

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.

Problem

• Byzantine-tolerant
• distributed learning
• finite mixture models
• partial corruptions
• component-wise Byzantine failure

Innovation

• Component-wise Byzantine failure
• Filtered mixture reduction
• Majority radius
• Distributed learning
• Finite mixture models