Kernel-based sparse regression with the correntropy-induced loss

The correntropy-induced loss (C-loss) has been employed in learning algorithms to improve their robustness to non-Gaussian noise and outliers recently. Despite its success on robust learning, only little work has been done to study the generalization performance of regularized regression with the C-loss. To enrich this theme, this paper investigates a kernel-based regression algorithm with the C-loss and ℓ1-regularizer in data dependent hypothesis spaces. The asymptotic learning rate is established for the proposed algorithm in terms of novel error decomposition and capacity-based analysis technique. The sparsity characterization of the derived predictor is studied theoretically. Empirical evaluations demonstrate its advantages over the related approaches.