Function Learning from Interpolation

Authors:
Martin Anthony;Peter L. Bartlett
Affiliations:
Department of Mathematics, The London School of Economics and Political Science, Houghton Street, London WC2A 2AE, England (e-mail: m.anthony@lse.ac.uk);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)
Venue:
Combinatorics, Probability and Computing
Year:
2000

Citing 9
Cited 7

A general lower bound on the number of examples needed for learning

Information and Computation
Learnability and the Vapnik-Chervonenkis dimension

Journal of the ACM (JACM)
Computational learning theory: an introduction

Computational learning theory: an introduction
Characterizations of learnability for classes of {O, …, n}-valued functions

COLT '92 Proceedings of the fifth annual workshop on Computational learning theory
Decision theoretic generalizations of the PAC model for neural net and other learning applications

Information and Computation
Occam's razor for functions

COLT '93 Proceedings of the sixth annual conference on Computational learning theory
Fat-shattering and the learnability of real-valued functions

COLT '94 Proceedings of the seventh annual conference on Computational learning theory
Efficient distribution-free learning of probabilistic concepts

Journal of Computer and System Sciences - Special issue: 31st IEEE conference on foundations of computer science, Oct. 22–24, 1990
Scale-sensitive dimensions, uniform convergence, and learnability

Journal of the ACM (JACM)

Generalization Error Bounds for Threshold Decision Lists

The Journal of Machine Learning Research
On the generalization error of fixed combinations of classifiers

Journal of Computer and System Sciences
Maximal width learning of binary functions

Theoretical Computer Science
Relaxed uncertainty relations and information processing

Quantum Information & Computation
Robust cutpoints in the logical analysis of numerical data

Discrete Applied Mathematics
Analysis of a multi-category classifier

Discrete Applied Mathematics
Learning bounds via sample width for classifiers on finite metric spaces

Theoretical Computer Science

Quantified Score

Hi-index	0.00

Visualization

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.