LOW-RANK TENSOR HUBER REGRESSION

摘要

Low-rank tensor regression has been well considered under general least squares framework, but it is highly sensitive to the outliers or heavy-tailed errors. To tackle this problem, we propose a low-rank tensor Huber regression model in which the tensor nuclear norm regularization is employed to characterize the low-rankness. The risk bound of the resulting estimator is established under mild assumptions. In addition, an efficient and stable alternating direction method of multipliers based algorithm is designed to solve the proposed model, and the global convergence as well as the computational complexity of the algorithm is also analyzed. Finally, numerical experiments conducted both on synthetic data with different types of noises and a real dataset illustrate the robustness and effectiveness of the approach. Especially when the noise is heavy-tailed or the coefficient tensor is low-rank, the mean square error of the estimator obtained by our model can be orders of magnitude better than several existing methods.