This paper provides a general result on controlling local Rademacher complexities, which captures in an elegant form to relate the complexities with constraint on the expected norm to the corresponding ones with constraint on the empirical norm. This result is convenient to apply in real applications and could yield refined local Rademacher complexity bounds for function classes satisfying gene...

From concentration inequalities for the suprema of Gaussian or Rademacher processes an inequality is derived. It is applied to sharpen existing and to derive novel bounds on the empirical Rademacher complexities of unit balls in various norms appearing in the context of structured sparsity and multitask dictionary learning or matrix factorization. A key role is played by the largest eigenvalue ...

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, ...

X iv :m at h/ 93 02 20 6v 1 [ m at h. FA ] 4 F eb 1 99 3 Comparing gaussian and Rademacher cotype for operators on the space of continous functions Marius Junge Abstract We will prove an abstract comparision principle which translates gaussian cotype in Rademacher cotype conditions and vice versa. More precisely, let 2<q<∞ and T : C(K) → F a linear, continous operator. 1. T is of gaussian cotyp...

Bounds are given for the empirical and expected Rademacher complexity of classes of linear transformations from a Hilbert space H to a …nite dimensional space. The results imply generalization guarantees for graph regularization and multi-task subspace learning. 1 Introduction Rademacher averages have been introduced to learning theory as an e¢ cient complexity measure for function classes, mot...

We give explicit, polynomial–time computable formulas for the number of integer points in any two– dimensional rational polygon. A rational polygon is one whose vertices have rational coordinates. We find that the basic building blocks of our formulas are Dedekind–Rademacher sums, which are polynomial–time computable finite Fourier series. As a by–product we rederive a reciprocity law for these...