VC dimension, fat-shattering dimension, rademacher averages, and their applications

Abstract

We consider several complexity measures which capture the difficulty of learning under the i.i.d. assumption. Among these measures are growth function and VC dimension, covering number and fat-shattering dimension, and Rademacher complexity from statistical learning theory. Relationships among these complexity measures, their connection to learning, and tools for bounding them are provided. For each complexity measure, a uniform upper bound on the generalization error of classification problems is presented.