Conformal Prediction Using Decision Trees

Conformal prediction is a relatively new framework in which the predictive models output sets of predictions with a bound on the error rate, i.e., in a classification context, the probability of excluding the correct class label is lower than a pre-defined significance level. An investigation of the use of decision trees within the conformal prediction framework is presented, with the overall purpose to determine the effect of different algorithmic choices, including split criterion, pruning scheme and way to calculate the probability estimates. Since the error rate is bounded by the framework, the most important property of conformal predictors is efficiency, which concerns minimizing the number of elements in the output prediction sets. Results from one of the largest empirical investigations to date within the conformal prediction framework are presented, showing that in order to optimize efficiency, the decision trees should be induced using no pruning and with smoothed probability estimates. The choice of split criterion to use for the actual induction of the trees did not turn out to have any major impact on the efficiency. Finally, the experimentation also showed that when using decision trees, standard inductive conformal prediction was as efficient as the recently suggested method cross-conformal prediction. This is an encouraging results since cross-conformal prediction uses several decision trees, thus sacrificing the interpretability of a single decision tree.