Multiple-output regression with high-order structure information

In this paper, we propose a new method to learn the regression coefficient matrix for multiple-output regression, which is inspired by multi-task learning. We attempt to incorporate high-order structure information among the regression coefficients into the estimated process of regression coefficient matrix, which is of great importance for multiple-output regression. Meanwhile, we also intend to describe the output structure with noise covariance matrix to assist in learning model parameters. Taking account of the real-world data often corrupted by noise, we place a constraint of minimizing norm on regression coefficient matrix to make it robust to noise. The experiments are conducted on three public available datasets, and the experimental results demonstrate the power of the proposed method against the state-of-the-art methods.