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Some theory for Fisher's linear discriminant function, `naive Bayes', and some alternatives when there are many more variables than observations
Open accessAbstract
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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Cited by
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Fan, J., & Lv, J. (2008) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/j.1467-9868.2008.00674.x · Cited by 2,711
Regularized estimation of large covariance matrices
Bickel, P. J., & Levina, E. (2008) · The Annals of Statistics · doi:10.1214/009053607000000758 · Cited by 934
Self-citationCovariance regularization by thresholding
Bickel, P. J., & Levina, E. (2008) · The Annals of Statistics · doi:10.1214/08-aos600 · Cited by 893
Self-citationSparse permutation invariant covariance estimation
Rothman, A. J., Bickel, P. J., Levina, E., & Zhu, J. (2008) · Electronic Journal of Statistics · doi:10.1214/08-ejs176 · Cited by 560
Self-citationGeneralized Thresholding of Large Covariance Matrices
Rothman, A. J., Levina, E., & Zhu, J. (2009) · Journal of the American Statistical Association · doi:10.1198/jasa.2009.0101 · Cited by 489
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Metadata
- Authors
- Bickel, P. J., & Levina, E.
- Venue
- Bernoulli
- Published
- 2004-12-01
- Volume
- 10
- Issue
- 6
- Pages
- 989-1010
- ISSN
- 1350-7265 (ISSN-L)
- OpenAlex
- W2118250684
- Cited by
- 548
- References
- 0
- FWCI
- 9.84
- Type
- journal article
- Language
- en
- Open access
- bronze
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