Sparse Additive Machine with Pinball Loss

Abstract Sparse additive models have shown promising performance for classification and variable selection in high-dimensional data analysis. However, existing methods are limited to the error metric associated with hinge loss, which are sensitive to noise around the decision boundary. In this paper, we propose a new sparse additive machine with the pinball loss, called as pin-SAM, to make the model more robust to noise around the decision boundary. Theoretical analysis on the excess misclassification error is established by integrating error decomposition and concentration estimation techniques, which shows our pin-SAM can achieve the fast learning rate under appropriate parameter conditions. The empirical studies confirm the effectiveness of the proposed approach on simulated, benchmark and coronal mass ejection data.