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December 2004 Some theory for Fisher's linear discriminant function, `naive Bayes', and some alternatives when there are many more variables than observations
Peter J. Bickel, Elizaveta Levina
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Bernoulli 10(6): 989-1010 (December 2004). DOI: 10.3150/bj/1106314847

Abstract

We show that the `naive Bayes' classifier which assumes independent covariates greatly outperforms the Fisher linear discriminant rule under broad conditions when the number of variables grows faster than the number of observations, in the classical problem of discriminating between two normal populations. We also introduce a class of rules spanning the range between independence and arbitrary dependence. These rules are shown to achieve Bayes consistency for the Gaussian `coloured noise' model and to adapt to a spectrum of convergence rates, which we conjecture to be minimax.

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Peter J. Bickel. Elizaveta Levina. "Some theory for Fisher's linear discriminant function, `naive Bayes', and some alternatives when there are many more variables than observations." Bernoulli 10 (6) 989 - 1010, December 2004. https://doi.org/10.3150/bj/1106314847

Information

Published: December 2004
First available in Project Euclid: 21 January 2005

zbMATH: 1064.62073
MathSciNet: MR2108040
Digital Object Identifier: 10.3150/bj/1106314847

Rights: Copyright © 2004 Bernoulli Society for Mathematical Statistics and Probability

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Vol.10 • No. 6 • December 2004
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