报告题目：Communication-Efficient Distributed Linear Discriminant Analysis for Binary Classification

报告时间：2023年10月13日（星期五）下午14:00-15:00

报告地点：沙河校区，二教205

报告人：赵俊龙，北京师范大学统计学院，教授

报告摘要：Large-scale data are common when the sample size n is large, and these data are often stored on k different local machines. Distributed statistical learning is an efficient way to deal with such data. In this study, we consider the binary classification problem for massive data based on a linear discriminant analysis (LDA) in a distributed learning framework. The classical centralized LDA requires the transmission of some p-by-p summary matrices to the hub, where p is the dimension of the variates under consideration. This can be a burden when p is large or the communication costs between the nodes are expensive. We consider two distributed LDA estimators, two-round and one-shot estimators, which are communication-efficient without transmitting p-by-p matrices. We study the asymptotic relative efficiency of distributed LDA estimators compared to a centralized LDA using random matrix theory under different settings of k. It is shown that when k is in a suitable range, such as k = o(n/p), these two distributed estimators achieve the same efficiency as that of the centralized estimator under mild conditions. Moreover, the two-round estimator can relax the restriction on k, allowing kp/n ->c \in [0, 1) under some conditions. Simulations confirm the theoretical results.

报告人简介：赵俊龙：北京师范大学统计学院教授。研究领域：高维数据分析、稳健统计，统计机器学习。在统计学各类期刊发表SCI论文近五十篇，部分结果发表在统计学顶级期刊Journal of the Royal Statistical Society: Series B（JRSSB）、The Annals of Statistics（AOS）、Journal of American Statistical Association(JASA)，Biometrika等。主持多项国家自然基金项目，参与国家自然科学基金重点项目。任中国现场统计学会高维数据分会、北京大数据学会等学术分会理事或常务理事。

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