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Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap

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  • Kim, Ji-Hyun

Abstract

We consider the accuracy estimation of a classifier constructed on a given training sample. The naive resubstitution estimate is known to have a downward bias problem. The traditional approach to tackling this bias problem is cross-validation. The bootstrap is another way to bring down the high variability of cross-validation. But a direct comparison of the two estimators, cross-validation and bootstrap, is not fair because the latter estimator requires much heavier computation. We performed an empirical study to compare the .632+ bootstrap estimator with the repeated 10-fold cross-validation and the repeated one-third holdout estimator. All the estimators were set to require about the same amount of computation. In the simulation study, the repeated 10-fold cross-validation estimator was found to have better performance than the .632+ bootstrap estimator when the classifier is highly adaptive to the training sample. We have also found that the .632+ bootstrap estimator suffers from a bias problem for large samples as well as for small samples.

Suggested Citation

  • Kim, Ji-Hyun, 2009. "Estimating classification error rate: Repeated cross-validation, repeated hold-out and bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 53(11), pages 3735-3745, September.
  • Handle: RePEc:eee:csdana:v:53:y:2009:i:11:p:3735-3745
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    References listed on IDEAS

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    1. G. Fitzmaurice & W. Krzanowski & D. Hand, 1991. "A Monte Carlo study of the 632 bootstrap estimator of error rate," Journal of Classification, Springer;The Classification Society, vol. 8(2), pages 239-250, December.
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    1. Chen, Weijie & Yousef, Waleed A. & Gallas, Brandon D. & Hsu, Elizabeth R. & Lababidi, Samir & Tang, Rong & Pennello, Gene A. & Symmans, W. Fraser & Pusztai, Lajos, 2012. "Uncertainty estimation with a finite dataset in the assessment of classification models," Computational Statistics & Data Analysis, Elsevier, vol. 56(5), pages 1016-1027.
    2. 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.
    3. Luts, Jan & Ormerod, John T., 2014. "Mean field variational Bayesian inference for support vector machine classification," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 163-176.
    4. Ha, Tran Vinh & Asada, Takumi & Arimura, Mikiharu, 2019. "Determination of the influence factors on household vehicle ownership patterns in Phnom Penh using statistical and machine learning methods," Journal of Transport Geography, Elsevier, vol. 78(C), pages 70-86.
    5. Likang Zheng & Junyuan Wang & Zhijian Wang & Wenhua Du, 2019. "Research on Novel Bearing Fault Diagnosis Method Based on Improved Krill Herd Algorithm and Kernel Extreme Learning Machine," Complexity, Hindawi, vol. 2019, pages 1-19, November.
    6. Conde, David & Fernández, Miguel & Salvador, Bonifacio & Rueda, Cristina, 2015. "dawai: An R Package for Discriminant Analysis with Additional Information," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 66(i10).
    7. I. Charvet & A. Suppasri & H. Kimura & D. Sugawara & F. Imamura, 2015. "A multivariate generalized linear tsunami fragility model for Kesennuma City based on maximum flow depths, velocities and debris impact, with evaluation of predictive accuracy," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 79(3), pages 2073-2099, December.
    8. Xue, Jing-Hao & Titterington, D. Michael, 2010. "On the generative-discriminative tradeoff approach: Interpretation, asymptotic efficiency and classification performance," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 438-451, February.
    9. Pyzhov, Vladislav & Pyzhov, Stanislav, 2017. "Comparison of methods of data mining techniques for the predictive accuracy," MPRA Paper 79326, University Library of Munich, Germany.
    10. Hosseini, Fatemeh & Eidsvik, Jo & Mohammadzadeh, Mohsen, 2011. "Approximate Bayesian inference in spatial GLMM with skew normal latent variables," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1791-1806, April.
    11. Matthias Schmid & Thomas Hielscher & Thomas Augustin & Olaf Gefeller, 2011. "A Robust Alternative to the Schemper–Henderson Estimator of Prediction Error," Biometrics, The International Biometric Society, vol. 67(2), pages 524-535, June.
    12. Gonzalo Perez-de-la-Cruz & Guillermina Eslava-Gomez, 2016. "Discriminant analysis with Gaussian graphical tree models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(2), pages 161-187, April.
    13. Gonzalo Perez-de-la-Cruz & Guillermina Eslava-Gomez, 2019. "Discriminant analysis for discrete variables derived from a tree-structured graphical model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 855-876, December.
    14. Khan, Jafar A. & Van Aelst, Stefan & Zamar, Ruben H., 2010. "Fast robust estimation of prediction error based on resampling," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3121-3130, December.
    15. Airola, Antti & Pahikkala, Tapio & Waegeman, Willem & De Baets, Bernard & Salakoski, Tapio, 2011. "An experimental comparison of cross-validation techniques for estimating the area under the ROC curve," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1828-1844, April.
    16. Usta, Ilhan & Kantar, Yeliz Mert, 2011. "On the performance of the flexible maximum entropy distributions within partially adaptive estimation," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2172-2182, June.
    17. Piccarreta, Raffaella, 2010. "Binary trees for dissimilarity data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1516-1524, June.

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