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Classification with decision trees from a nonparametric predictive inference perspective

Author

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  • Abellán, Joaquín
  • Baker, Rebecca M.
  • Coolen, Frank P.A.
  • Crossman, Richard J.
  • Masegosa, Andrés R.

Abstract

An application of nonparametric predictive inference for multinomial data (NPI) to classification tasks is presented. This model is applied to an established procedure for building classification trees using imprecise probabilities and uncertainty measures, thus far used only with the imprecise Dirichlet model (IDM), that is defined through the use of a parameter expressing previous knowledge. The accuracy of that procedure of classification has a significant dependence on the value of the parameter used when the IDM is applied. A detailed study involving 40 data sets shows that the procedure using the NPI model (which has no parameter dependence) obtains a better trade-off between accuracy and size of tree than does the procedure when the IDM is used, whatever the choice of parameter. In a bias-variance study of the errors, it is proved that the procedure with the NPI model has a lower variance than the one with the IDM, implying a lower level of over-fitting.

Suggested Citation

  • Abellán, Joaquín & Baker, Rebecca M. & Coolen, Frank P.A. & Crossman, Richard J. & Masegosa, Andrés R., 2014. "Classification with decision trees from a nonparametric predictive inference perspective," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 789-802.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:789-802
    DOI: 10.1016/j.csda.2013.02.009
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    References listed on IDEAS

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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. Hapfelmeier, A. & Ulm, K., 2013. "A new variable selection approach using Random Forests," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 50-69.
    3. Abellán, Joaquín & Baker, Rebecca M. & Coolen, Frank P.A., 2011. "Maximising entropy on the nonparametric predictive inference model for multinomial data," European Journal of Operational Research, Elsevier, vol. 212(1), pages 112-122, July.
    4. Abellán, Joaquín & Masegosa, Andrés R., 2010. "An ensemble method using credal decision trees," European Journal of Operational Research, Elsevier, vol. 205(1), pages 218-226, August.
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    Cited by:

    1. Frank PA Coolen & Tahani Coolen-Maturi & Abdullah H Al-nefaiee, 2014. "Nonparametric predictive inference for system reliability using the survival signature," Journal of Risk and Reliability, , vol. 228(5), pages 437-448, October.

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