【主题】Distributed Robust Estimation on Sparse  Linear Regression

【报告人】刘卫东, 教授

上海交通大学

【时间】 2019年6月26日（星期三）13:30-14:30

【地点】上海财经大学统计与管理学院大楼1208会议室

【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.

【嘉宾简介】刘卫东，上海交通大学教授，其研究领域包括：High dimensional statistical inference，Statistical methods for biostatistics，Nonlinear time series analysis

Nonparametric modeling，New statistical methods等。2018年入选国家杰出青年科学基金项目。

【主持人】尤进红