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讲座:Quantile Regression Under Memory Constraint

来源:上海交通大学安泰经济与管理学院 | 2018-10-12 | 发布:经管之家

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题目: Quantile Regression Under Memory Constraint

演讲人: 刘卫东 教授 上海交通大学自然科学研究院

主持人: 王彤 助理教授 上海交通大学安泰经济与管理学院运营管理系

时间: 2018年10月17日(周三)14:00-15:30

地 点: 上海交通大学徐汇校区 包图A303室


内容摘要:

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.

嘉宾简介:

Weidong Liu earned his Ph.D from Zhejiang University in 2008. During 2008-2009, he was a postdoctoral fellow in Hong Kong University of Science and Technology. After finishing postodoctoral research at HKUST, he joined Wharton School in University of Pennsylvania as a postdoctoral fellow. In 2011, he joined Shanghai Jiao Tong University. Weidong Liu has been awarded by National Excellent Doctoral Dissertation Award from China and New World Mathematics Awards, Silver Award for the Ph.D Thesis in 2010. His research interests are focused on statistics and probability. In high dimensional statistical inference, Weidong Liu and coauthors developed several new methods on the estimation of high dimensional covariance matrix/inverse matrix. In time series analysis and nonparametric estimation, he and coauthors had made important progress in several long-standing opening problems. Many of his research results were published in the top journals such as JASA、Ann.Stat.、Biometrika, Ann. Appl.Probab. and Probab Theor Relat Field.


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