Shrinkage Discriminant Analysis and CAT Score Variable Selection

sda page on CRAN.

This package provides an efficient framework for high-dimensional linear and diagonal discriminant analysis with variable selection. The classifier is trained using James-Stein-type shrinkage estimators and predictor variables are ranked using correlation-adjusted t-scores (CAT scores). Variable selection error is controlled using false non-discovery rates or higher criticism.

Current Version: 1.3.8

Authors: Miika Ahdesmäki, Verena Zuber, Sebastian Gibb, and Korbinian Strimmer.

Documentation and Installation:

Quick install: enter at the R console: install.packages("sda")

• Manual (pdf file) and release history.
• Download of sda version 1.3.8 source package.
• Archive of previous versions of sda.
• Licensed under the GNU GPL version 3 (or any later version).

Additional Material:

• Example R script for analyzing Khan et al. (2001) SRBCT data and corresponding PDF.
• Example R script for feature selection using Singh et al. (2002) prostate cancer data and corresponding PDF.
• R code for comparison of CAT score based variable selection with the leekasso.
  See the discussion at the simply statistics blog and the results using the sda package:
  

Relevant Publication:

• Ahdesmäki, M., and K. Strimmer. 2010. Feature selection in omics prediction problems using cat scores and false non-discovery rate control. Ann. Appl. Stat. 4: 503-519. (arXiv:0903.2003)
• Zuber, V., and K. Strimmer. 2009. Gene ranking and biomarker discovery under correlation. Bioinformatics 25: 2700-2707. (arXiv:0902.0751)
• A. Kessy, A. Lewin, and K. Strimmer. 2015. Optimal whitening and decorrelation. (arXiv:1512.00809)

Connection of CAT Scores with Optimal Whitening:

• See the example R scripts whiten.R and whiten-example.R. For a discussion of the optimality of the whitening procedure underlying the CAT score see A. Kessy, A. Lewin, and K. Strimmer. 2015. Optimal whitening and decorrelation. (arXiv:1512.00809).
• Essentially, there exists a unique whitening transformation with the property that the whitened variables are maximally correlated to the original variables. Computing CAT scores for the original data is identical to computing t-scores from the optimally whitened data (cf. example R scripts).

Misc:

• A related variable ranking approach for models with continuous response using CAR scores is implemented in the care package.
• In G. I. Allen and R. Tibshirani (2012) there is an extensive comparison of CAT scores with related statistics (Table 2).

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