|
NeuroCOLT
Technical Report NC-TR-94-013
Function
Learning from Interpolation
Martin
Anthony
Department of Mathematics
The London School of Economics and Political Science
Houghton Street
London WC2A 2AE
United Kingdom
Peter
Bartlett
Department of Systems Engineering
Research School of Information Sciences and Engineering
The Australian National University
Canberra, 0200 Australia
Abstract
In this paper, we study a statistical property of classes of real-valued
functions that we call approximation from interpolated examples. We
derive a characterization of function classes that have this property,
in terms of their `fat-shattering function', a notion that has proven
useful in computational learning theory. We discuss the implications
for function learning of approximation from interpolated examples.
Specifically, it can be interpreted as a problem of learning real-valued
functions from random examples in which we require satisfactory performance
from every algorithm that returns a function which approximately interpolates
the training examples.
Download Compressed
Postscript
|