After the learning phase we obtain a theory that classifies examples into one of the chosen intervals. The next step consists on using this learned theory to predict the class value of unseen instances. Given a discrete class (an interval) we want to obtain a value that will be used as our prediction. The standard procedure is to use a measure of centrality of the interval as prediction. In our experiments we use the median of the values that originated the interval.
We now address the problem of evaluating the predictive power of regression models. The standard procedure used to evaluate the accuracy of a theory consists on testing it on unseen data. On regression the prediction error e is given by the difference between the real value y and the predicted one . This methodology is very different from the one followed in classification problems. On these tasks errors are non-metric, i.e. a prediction is either correct or incorrect. Accuracy is thus a function of the number of errors. In regression the amplitude of errors is important.
There are several statistics that somehow try to characterize the accuracy of regression models. In our experiments we have chosed to work with two of them. One gives absolute estimates of the error (MAE) while the other provides relative estimates (MAPE) :
There are much more possibilities each having some advantages and some disadvantages. It is out of the scope of this paper to determine which one is more adequate to a given task.