Robust Multi-Task Regression with Shifting Low-Rank Patterns  

作　　者：Junfeng Cui Guanghui Wang Fengyi Song Xiaoyan Ma Changliang Zou 

机构地区：[1]School of Mathematical Sciences,Shenzhen University,Shenzhen 518060,P.R.China [2]NITFID,School of Statistics and Data Science,LPMC and KLMDASR and LEBPS,Nankai University,Tianjin 300071,P.R.China [3]School of Mathematics and Statistics,Ningxia University,Yinchuan 750021,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2025年第2期677-702,共26页数学学报(英文版)

基　　金：supported by the National Key R&D Program of China(Grant Nos.2022YFA1003703,2022YFA 1003800);the National Natural Science Foundation of China(Grant Nos.11925106,12231011,11931001,12226007,12326325);supported by the National Natural Science Foundation of China(Grant No.12301380);supported by the National Key R&D Program of China(Grant Nos.2021YFA1000100,2021YFA1000101,2022YFA1003800);the Natural Science Foundation of Shanghai(Grant No.23ZR1419400)。

摘　　要：We consider the problem of multi-task regression with time-varying low-rank patterns,where the collected data may be contaminated by heavy-tailed distributions and/or outliers.Our approach is based on a piecewise robust multi-task learning formulation,in which a robust loss function—not necessarily to be convex,but with a bounded derivative—is used,and each piecewise low-rank pattern is induced by a nuclear norm regularization term.We propose using the composite gradient descent algorithm to obtain stationary points within a data segment and employing the dynamic programming algorithm to determine the optimal segmentation.The theoretical properties of the detected number and time points of pattern shifts are studied under mild conditions.Numerical results confirm the effectiveness of our method.

关 键 词：Low-rank matrix estimation multiple change-point detection multi-task regression robust learning 

分 类 号：O17[理学—数学]