讲座题目：Byzantine—tolerant distributed learning of finite mixture models
主讲人：Jiahua Chen 教授
主持人：刘玉坤 教授
开始时间：2025-07-14 14:00
讲座地址：普陀校区理科大楼A512
主办单位：统计学院
报告人简介：
陈家骅，加拿大不列颠哥伦比亚大学（UBC）统计系国家一级讲座教授、加拿大皇家科学院院士。中国科大数学系本科，中国科学院系统科学研究所获得硕士学位，美国威斯康星大学麦迪逊分校统计学系获得博士学位，师从吴建福教授。研究兴趣包括有限混合模型、经验似然、统计遗传学、抽样调查、变量选择以及试验设计等多个统计研究领域，科研论文发表在国际统计学顶级期刊如JASA、JRSSB、Annals of Statistics、Biometrika、Statistica Sinica等。曾任泛华统计学会主席、加拿大统计杂志主编等职务。当选IMS和ASA fellow；2014年获加拿大统计学会最高奖--CRM-SSC统计学奖(该奖项由加拿大统计学会(SSC) 和蒙特利尔数学研究中心(CRM)联合主办，每年颁发给一位加拿大统计学家，以表彰他在获得博士学位后15年内对该学科的杰出贡献)；2016年获泛华统计协会杰出成就奖;2022年当选加拿大皇家科学院院士。
报告内容：
Traditional statistical methods must evolve to keep pace with modern distributed data storage systems. One widely used strategy is the split-and-conquer framework, where models are trained independently on local machines and their parameter estimates are then averaged. While effective for many problems, this approach breaks down when applied to finite mixture models due to the label switching problem---the arbitrary permutation of subpopulation labels across local machines. To tackle this, Mixture Reduction (MR) methods have been proposed, which help reconcile label mismatches. However, MR techniques are not resilient to Byzantine failures, where some local machines may send highly erroneous or even malicious outputs. This paper presents Distance Filtered Mixture Reduction (DFMR), a robust and efficient extension of MR designed to withstand Byzantine failure. DFMR introduces a novel filtering mechanism based on the distribution of local estimates. By computing pairwise $L^2$ distances between these estimates, DFMR identifies and discards outliers likely caused by corruption, while preserving the integrity of the majority. We offer theoretical guarantees for DFMR, demonstrating that it achieves the optimal convergence rate and is asymptotically equivalent to the global maximum likelihood estimate under standard conditions. Through experiments on both simulated and real-world datasets, we show that DFMR delivers reliable and accurate results even in adversarial environments. Collaborative work with Qiong Zhang and Yan Shuo Tan.
