Generalization Performance of Radial Basis Function Networks

This paper studies the generalization performance of radial basis function (RBF) networks using local Rademacher complexities. We propose a general result on controlling local Rademacher complexities with the L1 -metric capacity. We then apply this result to estimate the RBF networks' complexities, based on which a novel estimation error bound is obtained. An effective approximation error bound is also derived by carefully investigating the Hölder continuity of the lp loss function's derivative. Furthermore, it is demonstrated that the RBF network minimizing an appropriately constructed structural risk admits a significantly better learning rate when compared with the existing results. An empirical study is also performed to justify the application of our structural risk in model selection.