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

报 告 人：罗自炎教授（北京交通大学）

报告时间：2023年12月17日（周日）16:00-17:00

报告地点：龙洞校区行政楼610报告厅

主持人：陈智奇

报告摘要：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 an orthogonal decomposition, namely 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 TgSLOPE estimate risk. For efficient problem resolution, we equivalently transform the TgSLOPE problem into a difference-of-convex (DC) program with the level-coercive objective function. This allows us to solve the reformulation problem of TgSLOPE by an efficient proximal DC algorithm (DCA) with global convergence. Numerical studies conducted on synthetic data and a real human brain connection data illustrate the efficacy of the proposed TgSLOPE estimation procedure.

专家简介：罗自炎，北京交通大学数学与统计学院教授、博士生导师，中国运筹学会数学规划分会副秘书长，中国运筹学会女性工作委员会委员。曾为美国斯坦福大学、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等。发表SCI论文40余篇(ESI高被引论文2篇)，涉及《Math Program》《SIAM J Optim》《J Mach Learn Res》《IEEE Trans Signal Process》《SIAM J Matrix Anal Appl》等国际权威期刊。合作撰写美国SIAM出版社英文专著1部、中文著作1部；主持国家高层次人才特殊支持计划青年拔尖人才项目，国家自然科学基金“面上”、“青年”项目、北京市自然科学基金“重点”项目，参与国家自然科学基金“重点”项目，国家重点研发计划等。获教育部自然科学奖二等奖、中国运筹学会青年科技奖提名奖、北京市青年教师教学基本功比赛二等奖、北京市本科毕设论文优秀指导教师等。主要研究兴趣：大规模稀疏低秩优化、张量优化、机器学习，及其在压缩感知、视频分析、智慧交通中的应用