Multilinear Multitask Learning by Transformed Tensor Singular Value Decomposition

摘要：In this talk, we study the multilinear multitask learning problem, where all the tasks are combined and formed into a third-order tensor. Compared with traditional multitask learning, multilinear multitask learning can explore the intrinsic correlations among tasks better via the use of multilinear algebra. Existing methods for multilinear multitask learning are mainly based on the sum of nuclear norms of unfolding matrices of a tensor, which is suboptimal to approximate the Tucker rank of a tensor. In order to exploit the inherent correlations among related tasks further, we propose a transformed tensor nuclear norm (TTNN) constraint approach combined with a general loss function in the objective. The TTNN is used to generate a lower transformed multi-rank tensor by using suitable unitary transformations, and the transformation can help to determine principal components in grouping multitask. An excess risk bound of the estimator of the TTNN model is established. Numerical examples on synthetic data and real-world datasets are conducted to demonstrate the superiority of the proposed model over the existing methods.

张雄军,华中师范大学数学与统计学学院副教授，博士生导师. 2017年博士毕业于湖南大学, 2015年11月-2016年11月香港浸会大学博士交换生，2020年9月-2021年9月香港大学博士后，2019年获湖南省优秀博士学位论文.主要研究方向包括图像处理和张量优化,目前已在包括SIAM J. Imaging Sci., SIAM J. Sci. Comput., IEEE TIT, IEEE TPAMI, IEEE TNNLS, Inverse Problems等期刊发表论文20余篇.