Low-rank elastic-net regularized multivariate Huber regression model

摘要

Heavy-tailed noise or strongly correlated predictors often go with the multivariate linear regression model. To tackle with these problems, this paper focuses on the matrix elastic net regularized multivariate Huber regression model. This new model possesses the grouping effect property and the robustness to heavy-tailed noise. Meanwhile, it also has the ability of reducing the negative effect of outliers due to Huber loss. Furthermore, an accelerated proximal gradient algorithm is designed to solve the proposed model. Some numerical studies including a real data analysis are dedicated to show the efficiency of our method.