Boosting the margin: A new explanation for the effectiveness of voting methods
Schapire, R. E. , Freund, Y. , Bartlett, P.L., & Lee, W. S. (1998) Boosting the margin: A new explanation for the effectiveness of voting methods. The Annals of Statistics, 26(5), pp. 1651-1686.
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One of the surprising recurring phenomena observed in experiments with boosting is that the test error of the generated classifier usually does not increase as its size becomes very large, and often is observed to decrease even after the training error reaches zero. In this paper, we show that this phenomenon is related to the distribution of margins of the training examples with respect to the generated voting classification rule, where the margin of an example is simply the difference between the number of correct votes and the maximum number of votes received by any incorrect label. We show that techniques used in the analysis of Vapnik's support vector classifiers and of neural networks with small weights can be applied to voting methods to relate the margin distribution to the test error. We also show theoretically and experimentally that boosting is especially effective at increasing the margins of the training examples. Finally, we compare our explanation to those based on the bias-variance decomposition.
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|Item Type:||Journal Article|
|Additional Information:||Publisher PDF uploaded as it is a pre 2000 publication|
|Keywords:||Bagging, Boosting, Decision trees, Ensemble methods, Error-correcting, Markov chain, Monte Carlo, Neural networks, Output coding|
|Subjects:||Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)|
Australian and New Zealand Standard Research Classification > ECONOMICS (140000) > ECONOMETRICS (140300)
|Divisions:||Past > QUT Faculties & Divisions > Faculty of Science and Technology|
Past > Schools > Mathematical Sciences
|Copyright Owner:||Institute of Mathematical Statistics|
|Deposited On:||12 Aug 2011 12:36|
|Last Modified:||12 Aug 2011 12:36|
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