Robust support vector regression in the primal.

The classical support vector regressions (SVRs) are constructed based on convex loss functions. Since non-convex loss functions to a certain extent own superiority to convex ones in generalization performance and robustness, we propose a non-convex loss function for SVR, and then the concave-convex procedure is utilized to transform the non-convex optimization to convex one. In the following, a Newton-type optimization algorithm is developed to solve the proposed robust SVR in the primal, which can not only retain the sparseness of SVR but also oppress outliers in the training examples. The effectiveness, namely better generalization, is validated through experiments on synthetic and real-world benchmark data sets.