Classification with decision trees from a nonparametric predictive inference perspective

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.