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 l_p 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.