On the Practical Applicability of VC Dimension Bounds

This article addresses the question of whether some recent Vapnik-Chervonenkis (VC) dimension-based bounds on sample complexity can be regarded as a practical design tool. Specifically, we are interested in bounds on the sample complexity for the problem of training a pattern classifier such that we can expect it to perform valid generalization. Early results using the VC dimension, while being extremely powerful, suffered from the fact that their sample complexity predictions were rather impractical. More recent results have begun to improve the situation by attempting to take specific account of the precise algorithm used to train the classifier. We perform a series of experiments based on a task involving the classification of sets of vowel formant frequencies. The results of these experiments indicate that the more recent theories provide sample complexity predictions that are significantly more applicable in practice than those provided by earlier theories; however, we also find that the recent theories still have significant shortcomings.