Bounds for Learning the Kernel: Rademacher Chaos Complexity

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 principal theory of U-processes. Then, we discuss how to estimate the empirical Rademacher chaos complexity by well-established metric entropy integrals and pseudo-dimension of the set of candidate kernels. Finally, we establish satisfactory generalization bounds and misclassification error rates for learning Gaussian kernels and general radial basis kernels.