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.

          Quantifying Generalization in Linearly Weighted 
                           Neural Networks

                 Sean B. Holden and Martin Anthony

              Technical Report CUED/F-INFENG/TR113

	    Cambridge University Engineering Department 
		        Trumpington Street 
		        Cambridge CB2 1PZ 
			     England 


                             Abstract

The Vapnik-Chervonenkis Dimension has proven to be of great use in the 
theoretical study of generalization in artificial neural networks. The 
`probably approximately correct' learning framework is described and the 
importance of the VC dimension is illustrated. We then investigate the 
VC dimension of certain types of linearly weighted neural networks. First, 
we obtain bounds on the VC dimensions of radial basis function networks 
with basis functions of several types. Secondly, we calculate the VC 
dimension of polynomial discriminant functions defined over both real 
and binary-valued inputs.

************************ 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_tr113.ps.Z
ftp> quit
unix> uncompress holden_tr113.ps.Z
unix> lpr holden_tr113.ps (or however you print PostScript)

b) Via postal mail:

Request a hardcopy from

Sean B. Holden
Cambridge University Engineering Department, 
Trumpington Street, 
Cambridge CB2 1PZ,
England.

or email me: sbh at eng.cam.ac.uk

This report also appears as London School of Economics Mathematics 
Preprint number LSE-MPS-42, December, 1992.