AVERAGE-CASE LEARNING CURVES FOR RADIAL BASIS FUNCTION NETWORKS
Sean Holden and Mahesan Niranjan
The application of statistical physics to the study of the learning curves of feedforward connectionist networks has, to date, been concerned mostly with networks that do not include hidden layers. Recent work has extended the theory to networks such as committee machines and parity machines; however these are not networks that are often used in practice and an important direction for current and future research is the extension of the theory to practical connectionist networks. In this paper we investigate the learning curves of a class of networks that has been widely, and successfully applied to practical problems: the Gaussian radial basis function networks (RBFNs). We address the problem of learning linear and nonlinear, realizable and unrealizable, target rules from noise-free training examples using a stochastic training algorithm. Expressions for the generalization error, defined as the expected error for a network with a given set of parameters, are derived for general Gaussian RBFNs, for which all parameters, including centres and spread parameters, are adaptable. Specializing to the case of RBFNs with fixed basis functions we then study the learning curves for these networks in the limit of high temperature.
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