报告时间：2022/09/14 10:00-12:00

 

报告地点：腾讯会议603-968-225

 

报告题目：Group SLOPE Penalized CP Low-Rank Tensor Regression

 

报告摘要：In this talk, we aim to seek a selection and estimation procedure for a class of tensor regression problems with multivariate covariates and matrix responses, which can provide theoretical guarantees for model selection in finite samples. Considering the frontal slice sparsity and low-rankness inherited in the coefficient tensor, we formulate the regression procedure as a group SLOPE penalized low-rank tensor optimization problem based on CANDECOMP/PARAFAC (CP) decomposition, namely CP-TgSLOPE. This procedure provably controls the newly introduced tensor group false discovery rate (TgFDR), provided that the predictor matrix is column-orthogonal. Moreover, we establish the asymptotically minimax convergence with respect to the $\ell_2$-loss of CP-TgSLOPE estimator at the frontal slice level. For efficient problem resolution, we equivalently reformulate the CP-TgSLOPE problem into a difference-of-convex (DC) program with a level-coercive objective function. This allows us to solve the reformulation problem of CP-TgSLOPE by an efficient proximal DC algorithm (DCA) with global convergence. Numerical studies that conducted on synthetic data and a real human brain connection data illustrate the efficiency of the proposed CP-TgSLOPE estimation procedure.

 

报告人简介：罗自炎，女，北京交通大学数学与统计学院教授、博士生导师。美国斯坦福大学、新加坡国立大学、英国南安普顿大学访问学者；香港理工大学研究助理。SCI论文40余篇 (ESI高被引论文2篇)，发表在《Math Program》《J Mach Learn Res》《IEEE Trans Signal Process》《SIAM J Matrix Anal Appl》等权威期刊。合作撰写SIAM出版社英文专著1部、中文著作1部；主持国家自然科学基金“面上”、“青年”基金项目、北京市自然科学基金重点项目各1项。2016年北京运筹学年会特邀大会报告; 2017年第十一届全国数学规划学术会议青年专题特邀报告; 2020年亚太运筹学会Pre-APORS会议代表中国运筹学会做国家贡献论文报告；2020年获中国运筹学会青年科技奖提名奖；2021年北京市青年教师教学基本功比赛二等奖。主要研究兴趣：大规模稀疏低秩优化、二阶方法、张量优化、统计学习，及其在智慧交通、压缩感知、视频分析中的应用。