Complexity of hyperconcepts

In machine-learning, maximizing the sample margin can reduce the learning generalization error. Samples on which the target function has a large margin (γ) convey more information since they yield more accurate hypotheses. Let X be a finite domain and S denote the set of all samples S⊆X of fixed cardinality m. Let H be a class of hypotheses h on X. A hyperconcept h′ is defined as an indicator function for a set A⊆S of all samples on which the corresponding hypothesis h has a margin of at least γ. An estimate on the complexity of the class H′ of hyperconcepts h′ is obtained with explicit dependence on γ, the pseudo-dimension of H and m.