Upper Bounds on Averaged Sampling Numbers for General Model Classes

We investigate sampling numbers for essentially arbitrary star-shaped model classes. Although sampling numbers have been determined for a wide-variety of concrete model classes, to the best of our knowledge, abstract characterizations have not received much attention. We employ techniques developed in the context of nonparametric regression and empirical-process theory to derive novel upper bounds on the averaged sampling numbers for general model classes relying only on the knowledge of their entropy numbers. Our formulation provides an abstract characterization for upper bounds of these sampling numbers. Moreover, we show that any interpolator of the data that lies in the model class achieves this bound.