VC-Dimension and Rademacher Averages: From Statistical Learning Theory to Sampling Algorithms

Rademacher Averages and the Vapnik-Chervonenkis dimension are fundamental concepts from statistical learning theory. They allow to study simultaneous deviation bounds of empirical averages from their expectations for classes of functions, by considering properties of the functions, of their domain (the dataset), and of the sampling process. In this tutorial, we survey the use of Rademacher Averages and the VC-dimension in sampling-based algorithms for graph analysis and pattern mining. We start from their theoretical foundations at the core of machine learning, then show a generic recipe for formulating data mining problems in a way that allows to use these concepts in efficient randomized algorithms for those problems. Finally, we show examples of the application of the recipe to graph problems (connectivity, shortest paths, betweenness centrality) and pattern mining. Our goal is to expose the usefulness of these techniques for the data mining researcher, and to encourage research in the area.