Classification Accuracy Based on Observed Margin |
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Authors: | J Shawe-Taylor |
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Affiliation: | (1) Department of Computer Science, Royal Holloway, University of London, Egham, TW20 0EX, England. jst@dcs.rhbnc.ac.uk., UK |
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Abstract: | Following recent results 10] showing the importance of the fat-shattering dimension in explaining the beneficial effect
of a large margin on generalization performance, the current paper investigates how the margin on a test example can be used
to give greater certainty of correct classification in the distribution independent model. Hence, generalization analysis
is possible at three distinct phases, a priori using a standard pac analysis, after training based on properties of the chosen hypothesis 10], and finally in this paper
at testing based on properties of the test example. The results also show that even if the classifier does not classify all
of the training examples correctly, the fact that a new example has a larger margin than that on the misclassified test examples,
can be used to give very good estimates for the generalization performance in terms of the fat-shattering dimension measured
at a scale proportional to the excess margin. The estimate relies on a sufficiently large number of the correctly classified
training examples having a margin roughly equal to that used to estimate generalization, indicating that the corresponding
output values need to be ``well sampled.'
Received January 31, 1997; revised June 9, 1997, and July 18, 1997. |
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Keywords: | , Computational learning theory, Generalization, Fat-shattering, Large margin, Pac estimates, Agnostic learning, |
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