Data sparse nonparametric regression with epsilon-insensitive losses

Overview & Synopsis

Leveraging the celebrated support vector regression (SVR) method, we propose a unifying framework in order to deliver regression machines in reproducing kernel Hilbert spaces (RKHSs) with data sparsity. The central point is a new definition of epsilon-insensitivity, valid for many regression losses (including quantile and expectile regression) and their multivariate extensions. We show that the dual optimization problem to empirical risk minimization with epsilon-insensitivity involves a data sparse regularization. We also provide an analysis of the excess of risk as well as a randomized coordinate descent algorithm for solving the dual. Numerical experiments validate our approach.