Local Rademacher complexities

Local Rademacher Complexities

We propose new bounds on the error of learning algorithms in terms of a data-dependent notion of complexity. The estimates we establish give optimal rates and are based on a local and empirical version of Rademacher averages, in the sense that the Rademacher averages are computed from the data, on a subset of functions with small empirical error. We present some applications to classification, ...

Local Rademacher Complexities and Empirical Minimization

Localization of VC Classes: Beyond Local Rademacher Complexities

In statistical learning the excess risk of empirical risk minimization (ERM) is controlled by ( COMPn(F) n )α , where n is a size of a learning sample, COMPn(F) is a complexity term associated with a given class F and α ∈ [ 1 2 , 1] interpolates between slow and fast learning rates. In this paper we introduce an alternative localization approach for binary classification that leads to a novel c...

Localized Rademacher Complexities

We investigate the behaviour of global and local Rademacher averages. We present new error bounds which are based on the local averages and indicate how data-dependent local averages can be estimated without a priori knowledge of the class at hand.

Discussion: Local Rademacher Complexities and Oracle Inequalities in Risk Minimization

In this magnificent paper, Professor Koltchinskii offers general and powerful performance bounds for empirical risk minimization, a fundamental principle of statistical learning theory. Since the elegant pioneering work of Vapnik and Chervonenkis in the early 1970s, various such bounds have been known that relate the performance of empirical risk minimizers to combinatorial and geometrical feat...