Abstract for holden_tr212

Cambridge University Engineering Department Technical Report CUED/F-INFENG/TR212

AVERAGE-CASE LEARNING CURVES FOR RADIAL BASIS FUNCTION NETWORKS

Sean Holden and Mahesan Niranjan

May 1995

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.


(ftp:) holden_tr212.ps.Z (http:) holden_tr212.ps.Z
PDF (automatically generated from original PostScript document - may be badly aliased on screen):
  (ftp:) holden_tr212.pdf | (http:) holden_tr212.pdf

If you have difficulty viewing files that end '.gz', which are gzip compressed, then you may be able to find tools to uncompress them at the gzip web site.

If you have difficulty viewing files that are in PostScript, (ending '.ps' or '.ps.gz'), then you may be able to find tools to view them at the gsview web site.

We have attempted to provide automatically generated PDF copies of documents for which only PostScript versions have previously been available. These are clearly marked in the database - due to the nature of the automatic conversion process, they are likely to be badly aliased when viewed at default resolution on screen by acroread.