Results on learnability and the Vapnik-Chervonenkis dimension

The problem of learning a concept from examples in a distribution-free model is considered. The notion of dynamic sampling, wherein the number of examples examined can increase with the complexity of the target concept, is introduced. This method is used to establish the learnability of various concept classes with an infinite Vapnik-Chervonenkis (VC) dimension. An important variation on the problem of learning from examples, called approximating from examples, is also discussed. The problem of computing the VC dimension of a finite concept set defined on a finite domain is considered.