时 间：2019年6月25日(周二)16：00-17：00
地 点：中北校区理科大楼A1716报告厅
题 目：Distributed Robust Estimation on Sparse Linear Regression
报告人：刘卫东，上海交通大学教授
摘 要：
This paper studies distributed estimation and support recovery for high-dimensional linear regression model with heavy-tailed noise. To deal with heavy-tailed noise whose variance can be infinite, we adopt the quantile regression loss function instead of the commonly used squared loss. However, the non-smooth quantile loss poses new challenges to high-dimensional distributed estimation in both computation and theoretical development. To address the challenge, we transform the response variable and establish a new connection between quantile regression and ordinary linear regression. Then, we provide a distributed estimator that is both computationally and communicationally efficient, where only the gradient information is communicated at each iteration. Theoretically, we show that the proposed estimator achieves the optimal convergence rate (i.e., the oracle convergence rate when all the data is pooled on a single machine) without any restriction on the number of machines. Moreover, we establish the theoretical guarantee for the support recovery. The simulation and real data analysis are provided to demonstrate the effectiveness of our estimator.
报告人简介：刘卫东，上海交通大学致远学院教授、博导，数学科学学院教授，副院长。浙江大学博士，香港科技大学、宾州大学沃顿商学院博士后。长期从事概率论与数理统计的科学研究，在概率年刊和统计学四大等高水平期刊发表论文40余篇。国家杰青（2018）。