The Robust Row Sparse Huber Matrix Regression

With the advent of the big data era,large amounts of high-dimensional matrix data is produced in various fields.And it leads to the emergence of high-dimensional matrix regression models.Considering the special structure of data,the solutions of the matrix regression models will have different properties(such as low rank,sparseness,etc.),so regularized matrix regression models have been studied a lot.In addition,data that contains outliers or heavy-tailed errors is commonly encountered,so it is particularly important to establish a model that matching the above-mentioned data.To simultaneously characterize the row sparsity of the solution and process the data with heavy-tailed error,in this paper,we propose a robust row sparse matrix regression model,discuss its theoretical properties and calculation results.First,we establish the robust row sparse Huber matrix regression model,which can describe the row sparsity of the solution and has robust estimation.Second,we give the theoretical properties of the model,which is resistance to outliers and upper bound of risk.From a statistical point of view,the robustness and feasibility of the model are guaranteed.In order to solve the high complexity of model solving and data storage problems in high-dimensional situations,inspired by the screening rule in the vector form and based on the dual theory of the model,we establish the screening rule of the model in the matrix form,which can be used for data preprocessing to accelerate the model solving.Finally,through simulated numerical experiments and real numerical experiments,it is proved that our screening rule has a good acceleration model performance under high-dimensional data.