MULTIVARIATE LINEAR REGRESSION WITH LOW-RANK AND ROW-SPARSITY

摘要

In the era of big data, multivariate linear regression (MLR) model emerges from many modern science and technology fields, such as gene expression analysis, brain neural network, finance, economics, medical imaging diagnosis, risk management and so on. In these high-dimensional data, the data often have some low-rank structure in order to catch the most material information. Meanwhile, some data sets show the block-character in predictors. Combining these two aspects, we propose a new matrix regression model in this paper. The proposed model can induce an estimator which is low-rank and sparse in the sense of row-group with the help of nuclear norm and parallel to.parallel to(2,1 )norm. In order to obtain an estimator, we develop a linearized alternating direction method of multipliers and prove its global convergency. Moreover, we adopt an efficient method for the tuning parameter selection. Finally, some numerical experiments are carried out to demonstrate the properties of the new proposed model and the accuracy of the proposed algorithm.