  The huge amount of available data nowadays is a challenge for kernel-based
machine learning algorithms like SVMs with respect to runtime and storage
capacities. Local approaches might help to relieve these issues and to improve
statistical accuracy. It has already been shown that these local approaches are
consistent and robust in a basic sense. This article refines the analysis of
robustness properties towards the so-called influence function which expresses
the differentiability of the learning method: We show that there is a
differentiable dependency of our locally learned predictor on the underlying
distribution. The assumptions of the proven theorems can be verified without
knowing anything about this distribution. This makes the results interesting
also from an applied point of view.
