报告题目：Quantile Regression Under Memory Constraint

报告人：刘卫东   上海交通大学教授

报告时间：2018年10月20日 10:00-11:00

报告地点：知新楼B1238

报告摘要：

This paper studies the inference problem in quantile regression (QR) for a large sample size $n$ but under a limited memory constraint, where the memory can only store a small batch of data of size $m$. A natural method is the na\”ive divide-and-conquer approach, which splits data into batches of size $m$, computes the local QR estimator for each batch, and then aggregates the estimators via averaging. However, this method only works when $n=o(m^2)$ and is computationally expensive. This paper proposes a computationally efficient method, which only requires an initial QR estimator on a small batch of data and then successively refines the estimator via multiple rounds of aggregations.

Theoretically, as long as $n$ grows polynomially in $m$, we establish the asymptotic normality for the obtained estimator and show that our estimator with only a few rounds of aggregations achieves the same efficiency as the QR estimator computed on all the data. Moreover, our result allows the case that the dimensionality $p$ goes to infinity. The proposed method can also be applied to address the QR problem under distributed computing environment (e.g., in a large-scale sensor network) or for real-time streaming data.

报告人简介：刘卫东教授，1981年生，2008年于浙江大学概率论与数理统计专业取得理学博士学位。2011年任上海交通大学教授。研究兴趣涉及高维统计推断，生物统计，非参数时间序列，概率极限理论等。2006年以来，刘卫东教授在Annals of Statistics, Journal of the Royal Statistical Society ，Journal of the American Statistical Association，Biometrika，Probability Theory and Related Fields, Annals of Probability, Annals of Applied Probability等概率统计顶级杂志发表论文19篇。曾获2010年全国百篇优秀博士论文奖，2010年新世界数学银奖。先后获得国家自然科学基金委优秀青年基金，杰出青年基金资助。

邀请人：王汉超