Rademacher complexity is a measure of the richness of a class of real-valued functions. In this sense, it is similar to the VC dimension. In fact, we will establish a uniform deviation bound in terms of Rademacher complexity, and then use this result to prove the VC inequality. Unlike VC dimension, however, Rademacher complexity is not restricted to binary functions, and will also prove useful ...

In this paper we describe the use of Rademacher penalization for model selection. As in Vapnik's Guaranteed Risk Minimization (GRM), Rademacher penalization attemps to balance the complexity of the model with its t to the data by minimizing the sum of the training error and a penalty term, which is an upper bound on the absolute di erence between the training error and the generalization error....

where σ1, ...σn are iid Rademacher random variables. Rn(F ) characterizes the extent to which the functions in F can be best correlated with a Rademacher noise sequence. A number of generalization error bounds have been proposed based on Rademacher complexity [1,2]. In this open problem, we introduce a new complexity measure for function classes. We focus on function classes F that is the conve...

We show how to control the generalization error of time series models wherein past values of the outcome are used to predict future values. The results are based on a generalization of standard i.i.d. concentration inequalities to dependent data without the mixing assumptions common in the time series setting. Our proof and the result are simpler than previous analyses with dependent data or st...

In his book Topics in Analytic Number Theory, Hans Rademacher conjectured that the limits of certain sequences of coefficients that arise in the ordinary partial fraction decomposition of the generating function for partitions of integers into at most N parts exist and equal particular values that he specifies. Despite being open for nearly four decades, little progress has been made toward pro...

In this paper we develop a novel probabilistic generalization bound for regularized kernel learning algorithms. First, we show that generalization analysis of kernel learning algorithms reduces to investigation of the suprema of homogeneous Rademacher chaos process of order two over candidate kernels, which we refer to it as Rademacher chaos complexity. Our new methodology is based on the princ...

In this paper we develop a novel probabilistic generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning algorithms reduces to investigation of the suprema of the Rademacher chaos process of order two over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rademacher ...

We develop a novel generalization bound for learning the kernel problem. First, we show that the generalization analysis of the kernel learning problem reduces to investigation of the suprema of the Rademacher chaos process of order 2 over candidate kernels, which we refer to as Rademacher chaos complexity. Next, we show how to estimate the empirical Rademacher chaos complexity by well-establis...

This paper examines the problem of learning with a finite and possibly large set of p base kernels. It presents a theoretical and empirical analysis of an approach addressing this problem based on ensembles of kernel predictors. This includes novel theoretical guarantees based on the Rademacher complexity of the corresponding hypothesis sets, the introduction and analysis of a learning algorith...