STAT-DS Invited Talks

High-dimensional tensor quantile regression

Speaker:Prof. Heng LIAN,City University of Hong Kong

Time:Nov 19, 2020, 16:00-17:00

Location:Tencent Meeting ID: 231 992 556

报告简介  Abstract

Quantile regression is an indispensable tool for statistical learning. Traditional quantile regression methods consider vector-valued covariates and estimate the corresponding coefficient vector. Many modern applications involve data with a tensor structure. We propose a quantile regression model which takes tensors as covariates and present an estimation approach based on Tucker decomposition. It effectively reduces the number of parameters, leading to efficient estimation and feasible computation. We also introduce a sparse Tucker decomposition to further reduce the number of parameters when the dimension of the tensor is large. We propose an alternating update algorithm combined with alternating direction method of multipliers (ADMM). The asymptotic properties of the estimators are established under suitable conditions. The numerical performances are demonstrated via simulations and an application to a crowd density estimation problem.

嘉宾简介  About the Speaker

练恒,现任香港城市大学数学系副教授,于2000年在中国科学技术大学获得数学和计算机学士学位,2007年在美国布朗大学获得计算机硕士,经济学硕士和应用数学博士学位。先后在新加坡南洋理工大学,澳大利亚新南威尔士大学,和香港城市大学工作。在高水平国际期刊上发表学术论文30多篇,包括《Annals of Statistics》《Journal of the Royal Statistical Society,Series B》、《Journal of the American Statistical Association》《Journal of Machine Learning Research》《IEEE Transactions on Pattern Analysis and Machine Intelligence》. 研究方向包括高维数据分析,函数数据分析,机器学习等。

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