Complexity dimensions and learnability

Abstract

In a discussion of the Vapnik Chervonenkis (VC) dimension ([7]), which is closely related to the learnability of concept classes in Valiant’s PAC-model ([6]), we win give an algorithm to compute it. Furthermore, we will take Natarajan’s equivalent dimension for well-ordered classes into a more general scheme, by showing that these well-ordered classes happen to satisfy some general condition, which makes it possible to construct for a class a number of equivalent dimensions. We will give this condition, as well as a relatively efficient algorithm for the calculation of one such dimension for well-ordered classes.