An incremental multivariate regression method for function approximation from noisy data

In this paper we consider the problem of approximating functions from noisy data. We propose an incremental supervised learning algorithm for RBF networks. Hidden gaussian nodes are added in an iterative manner during the training process. For each new node added, the activation function center and the output connection weight are settled according to an extended chained version of the Nadaraja-Watson estimator. Then the variances of the activation functions are determined by an empirical risk driven rule based on a genetic-like optimization technique.