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Function Learning from Interpolation

Published online by Cambridge University Press:  01 May 2000

MARTIN ANTHONY
Affiliation:
Department of Mathematics, The London School of Economics and Political Science, Houghton Street, London WC2A 2AE, England (e-mail: m.anthony@lse.ac.uk)
PETER L. BARTLETT
Affiliation:
Department of Systems Engineering, Research School of Information Sciences and Engineering, The Australian National University, Canberra, 0200 Australia (e-mail: Peter.Bartlett@anu.edu.au)

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 proved useful in computational learning theory. The property is central to 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.

Type
Research Article
Copyright
2000 Cambridge University Press

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