永利总站ylzz55 20230621：Group SLOPE Penalized Low-Rank Tensor Regression

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

报告人：罗自炎 教授（北京交通大学数学与统计学院）

报告摘要：In this talk, we aim to seek a selection and estimation procedure for a class of tensor regression problemss 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 tensor 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 L2-loss of TgSLOPE estimator at the frontal slice level. For efficient problem resolution, we equivalently reformulate the TgSLOPE problem into a difference-of-convex (DC) program with a level-coercive objective function, This allows us to solve the reformulation problem of TeSLOPE by an effcient proxima 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 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，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》《JMach Learn IRes》《IEEE Trans Sigmal Process》《SIAMJMatrix AnalAppl》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。

报告时间：2023年6月21日 11:00-12:00

报告地点：永利总站ylzz55 210

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2023年6月19日