REGULARIZED KERNEL NETWORKS WITH CONVEX P-LIPSCHITZ LOSS

.We propose a loss function class called convex p-Lipschitz loss functions, which includes hinge loss, pinball loss and least square loss and so on. For regularized kernel networks and bias corrected regularized kernel networks with general convex pLipschitz loss, we establish the error analysis frameworks by employing the leave one out technique [16]. Under a mild source condition which describes how the minimizer f* of the generalization error can be approximated by the hypothesis space HK, satisfying error bounds and learning rates are deduced. Moreover, our proofs also show that bias correction method can indeed decrease the learning error.