報告題目：High-dimensional Quantile Tensor Regression

演講人🛹🌟：朱仲義復旦大學教授，博士生導師

報告時間：2021年4月9日（周五）14:00-15:30

報告地點：凯捷体育注册335

摘要：Quantile regression is an indispensable tool for statisticallearning. Traditional  quantile regression methods consider vector-valuedcovariates and estimate the corresponding coefficient vector. Many modernapplications involve data with a tensor structure. In this paper, we propose aquantile regression model which takes tensors as covariates, and present anestimation approach based on Tucker decomposition. It effectively reduces thenumber of parameters, leading to efficient estimation and feasible computation. We also use a sparse Tucker decomposition, which is a popular approach in theliterature, to further reduce the number of parameters when the dimension ofthe tensor is large. We propose an alternating update algorithm combined withalternating direction method of multipliers (ADMM). The asymptotic propertiesof the estimators are established under suitable conditions. The numericalperformances are demonstrated via simulations and an application to a crowddensity estimation problem.

演講人簡介：朱仲義教授是復旦大學管理凯捷統計系教授，博士生導師；曾任中國概率統計學會第八、九屆副理事長,國際著名雜誌”Statistica Sinica”副主編; “應用概率統計”, “數理統計與管理”雜誌編委👠↘️，中國統計教材編審委員會委員；現為Elected Member of the ISI（國際數理統計學會）🙇🏽；  ”中國科學：數學”雜誌編委。專業研究方向為💆🏽：保險精算；縱向數據(面板數據)模型；分位數回歸模型等。主持完成國家自然科學基金四項📆🕵🏽、國家社會科學基金一項，作為子項目負責人完成國家自然科學基金重點項目一項🤴🏿。目前主持國家自然科學基金重大項目子項目一項𓀄，重點項目子項目一項，面上項目一項。近幾年發表論文100多篇(其中包括在國際頂級刊物：J.R.Stat.Soc B, J.A.S.A., Ann. Statist. 和Biometrika等SCI論文五十多篇) 。第一完成人獲得教育部自然科學二等獎一次👏🏻。