Classification with decision trees from a nonparametric predictive inference perspective

Abellán, J.; Baker, R.M.; Coolen, F.P.A.; Crossman, R.J.; Masegosa, A.R.

doi:10.1016/j.csda.2013.02.009

Classification with decision trees from a nonparametric predictive inference perspective

Abellán, J.; Baker, R.M.; Coolen, F.P.A.; Crossman, R.J.; Masegosa, A.R.

Authors

J. Abellán

R.M. Baker

Professor Frank Coolen frank.coolen@durham.ac.uk
Professor

R.J. Crossman

A.R. Masegosa

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.

Citation

Abellán, J., Baker, R., Coolen, F., Crossman, R., & Masegosa, A. (2014). Classification with decision trees from a nonparametric predictive inference perspective. Computational Statistics & Data Analysis, 71, 789-802. https://doi.org/10.1016/j.csda.2013.02.009

Journal Article Type	Article
Publication Date	Mar 1, 2014
Deposit Date	Sep 13, 2013
Publicly Available Date	Nov 28, 2014
Journal	Computational Statistics & Data Analysis
Print ISSN	0167-9473
Publisher	Elsevier
Peer Reviewed	Peer Reviewed
Volume	71
Pages	789-802
DOI	https://doi.org/10.1016/j.csda.2013.02.009
Keywords	Imprecise probabilities, Imprecise Dirichlet model, Nonparametric predictive inference model, Uncertainty measures, Supervised classification, Decision trees.

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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Computational Statistics & Data Analysis. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computational Statistics & Data Analysis, 71, March 2014, 10.1016/j.csda.2013.02.009.