Distribution-free performance bounds with the resubstitution error estimate

Two distribution-free upper bounds are given for the true error rate of a classifier, using the resubstitution error estimate. These bounds apply when the classifier is selected from a finite decision rule set. Both improve a bound proposed by Vapnik (1982). One of them is in a way optimal, while ho...

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Bibliographic Details
Published in:Pattern recognition letters 1992-11, Vol.13 (11), p.757-764
Main Authors: Gascuel, Olivier, Caraux, Gilles
Format: Article
Language:English
Subjects:
Applied sciences
Artificial intelligence
classification trees
Computer science
control theory
systems
deterministic statement
Estimation of misclassification
Exact sciences and technology
histogram discrimination rules
Pattern recognition. Digital image processing. Computational geometry
resubstitution error estimate
uniform convergence
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Summary:Two distribution-free upper bounds are given for the true error rate of a classifier, using the resubstitution error estimate. These bounds apply when the classifier is selected from a finite decision rule set. Both improve a bound proposed by Vapnik (1982). One of them is in a way optimal, while however presenting the disadvantage to be not analytic and requiring to be computed numerically for a given situation. A quantitative comparison of these bounds is provided, with realistic parameter values taken from classification trees and histogram discrimination rules.
ISSN:0167-8655
1872-7344
DOI:10.1016/0167-8655(92)90125-J