New technical report

[S.B. Holden]

The following technical report is available by anonymous ftp from the
archive of the Speech, Vision and Robotics Group at the Cambridge
University Engineering Department.

              Average-Case Learning Curves for Radial 
                     Basis Function Networks


                Sean B. Holden and Mahesan Niranjan

               Technical Report CUED/F-INFENG/TR.212

	    Cambridge University Engineering Department 
		        Trumpington Street 
		        Cambridge CB2 1PZ 
			     England 


                             Abstract

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.

************************ How to obtain a copy ************************

a) Via FTP:

unix> ftp svr-ftp.eng.cam.ac.uk
Name: anonymous
Password: (type your email address)
ftp> cd reports
ftp> binary
ftp> get holden_tr212.ps.Z
ftp> quit
unix> uncompress holden_tr212.ps.Z
unix> lpr holden_tr212.ps (or however you print PostScript)

b) Via postal mail:

Request a hardcopy from

Dr. Sean B. Holden
Department of Computer Science
University College London
Gower Street
London WC1E 6BT
U.K.

or email me: s.holden at cs.ucl.ac.uk