This paper proposes two split-and-conquer (SC) learning estimators for finite mixture models that are tolerant to Byzantine failures. In SC learning, individual machines obtain local estimates, which are then transmitted to a central server for aggregation. During this communication, the server may receive malicious or incorrect information from some local machines, a scenario known as Byzantine failures. While SC learning approaches have been devised to mitigate Byzantine failures in statistical models with Euclidean parameters, developing Byzantine-tolerant methods for finite mixture models with non-Euclidean parameters requires a distinct strategy. Our proposed distance-based methods are hyperparameter tuning free, unlike existing methods, and are resilient to Byzantine failures while achieving high statistical efficiency. We validate the effectiveness of our methods both theoretically and empirically via experiments on simulated and real data from machine learning applications for digit recognition. The code for the experiment can be found at https://github.com/SarahQiong/RobustSCGMM.

翻译：本文提出了两种针对有限混合模型的拜占庭容错分割-征服学习估计器。在分割-征服学习中，各独立机器先获得局部估计，随后将结果传输至中央服务器进行聚合。在此通信过程中，服务器可能从部分本地机器接收到恶意或错误信息，该场景被称为拜占庭故障。虽然针对欧几里得参数统计模型的拜占庭故障缓解方法已有分割-征服学习方案，但针对非欧几里得参数有限混合模型开发拜占庭容错方法需要采用独特的策略。与现有方法不同，我们提出的基于距离的方法无需超参数调优，在实现高统计效率的同时保持对拜占庭故障的鲁棒性。我们通过机器学习数字识别应用的模拟数据和真实数据实验，从理论和实证两方面验证了所提方法的有效性。实验代码可在 https://github.com/SarahQiong/RobustSCGMM 获取。