Error bound for Slope SVM in High Dimension

In this paper, we propose a new estimator: the Slope SVM, which minimizes the hinge loss with the Slope penalization introduced by [3]. We study the asymptotical behavior of the `2 error between the theoretical hinge loss minimizer and the Slope estimator. We prove Slope achieves a (k/n) log(p/k) rate with high probability and in expectation under the Weighted Restricted Eigenvalue Condition. This bound is similar to the exact minimax one for regression and, to the best of our knowledge, it is the best achievable for a classification estimator.