Total stability of kernel methods

The paper gives conditions under which classical kernel based methods based on a convex Lipschitz loss function and on a bounded and smooth kernel are stable, if the probability measure P, the regularization parameter λ, and the kernel K may slightly change in a simultaneous manner. Similar results are also given for pairwise learning. Therefore, the topic of this paper is somewhat more general than in classical robust statistics, where usually only the influence of small perturbations of the probability measure P on the estimated function is considered.