A Deep Connection Between the Vapnik–Chervonenkis Entropy and the Rademacher Complexity

In this paper, we derive a deep connection between the Vapnik-Chervonenkis (VC) entropy and the Rademacher complexity. For this purpose, we first refine some previously known relationships between the two notions of complexity and then derive new results, which allow computing an admissible range for the Rademacher complexity, given a value of the VC-entropy, and vice versa. The approach adopted in this paper is new and relies on the careful analysis of the combinatorial nature of the problem. The obtained results improve the state of the art on this research topic.