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2011

Discriminant Analysis with Adaptively Pooled Covariance

Simon, Noah, Tibshirani, Rob

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Understand

Linear and Quadratic Discriminant analysis (LDA/QDA) are common tools for classification problems.

For these methods we assume observations are normally distributed within group.
We estimate a mean and covariance matrix for each group and classify using Bayes theorem.
With LDA, we estimate a single, pooled covariance matrix, while for QDA we estimate a separate covariance matrix for each group.

Discriminant Analysis with Adaptively Pooled Covariance · Around

Built on

Regularized discriminant analysis
J. Friedman · 1989
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Regression shrinkage and selection via the lasso
R. Tibshirani · 1996
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Atomic decomposition by basis pursuit
S. S. Chen, D. L. Donoho, and M. A. Saunders · 1998
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Comparison of discrimination methods for the classification of tumors using gene expression data
S. Dudoit, J. Fridlyand, and T. Speed · 2002
Earlier work this paper cites.
Some theory for fisher’s linear discriminant function,’naive bayes’, and some alternatives when there are many more variables than observations
P. Bickel and E. Levina · 2004
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