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Estimation of the conditional risk in classification: The swapping method

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  • Daudin, Jean-Jacques
  • Mary-Huard, Tristan

Abstract

The bias of the empirical error rate in supervised classification is studied. It is shown that this bias can be understood as a covariance between the classification rule and the labeling of the training data. From this result, a new penalized criterion is proposed to perform model selection in classification. Applications of the resulting algorithm to simulated and real data are presented.

Suggested Citation

  • Daudin, Jean-Jacques & Mary-Huard, Tristan, 2008. "Estimation of the conditional risk in classification: The swapping method," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3220-3232, February.
    • Handle: RePEc:eee:csdana:v:52:y:2008:i:6:p:3220-3232
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    References listed on IDEAS

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    1. Ghosh, Anil K., 2006. "On optimum choice of k in nearest neighbor classification," Computational Statistics & Data Analysis, Elsevier, vol. 50(11), pages 3113-3123, July.
    2. Bradley Efron, 2004. "The Estimation of Prediction Error: Covariance Penalties and Cross-Validation," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 619-632, January.
    3. Robert Tibshirani & Keith Knight, 1999. "The Covariance Inflation Criterion for Adaptive Model Selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 529-546.
    4. Dudoit S. & Fridlyand J. & Speed T. P, 2002. "Comparison of Discrimination Methods for the Classification of Tumors Using Gene Expression Data," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 77-87, March.
    5. Peter L. Bartlett & Stéphane Boucheron & Gábor Lugosi, 2000. "Model selection and error estimation," Economics Working Papers 508, Department of Economics and Business, Universitat Pompeu Fabra.
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    1. Borra, Simone & Di Ciaccio, Agostino, 2010. "Measuring the prediction error. A comparison of cross-validation, bootstrap and covariance penalty methods," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 2976-2989, December.

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