On learning and computational complexity of FIR radial basis function networks. Part I. Learning of FIR RBFN´s

Recently, the complexity control of dynamic neural models has gained significant attention from signal processing community. The performance of such a process depends highly on the applied definition of "model complexity", i.e. complexity models that give simpler networks with better model accuracy and reliability are preferred. The learning theory creates a framework to assess the learning properties of models. These properties include the required size of the training samples as well as the statistical confidence over the model. In this paper, we apply the learning properties of two families of FIR radial basis function networks (RBFN\´s) to introduce new complexity measures that reflect the learning properties of such neural models. Then, based on these complexity terms, we define cost functions, which provide a balance between the training and testing performances of the model, and give desirable levels of accuracy and confidence