Statistical Learning Theory

Abstract

This chapter presents an overview of statistical learning theory, and describes key results regarding uniform convergence of empirical means and related sample complexity. This theory provides a fundamental extension of the probability inequalities studied in Chap. 8 to the case when parameterized families of functions are considered, instead of a fixed function. The chapter formally studies the UCEM (uniform convergence of empirical means) property and the VC dimension in the context of the Vapnik–Chervonenkis theory. Extensions to the Pollard theory for continuous-valued functions are also discussed.