## 3 Experimental Results
The classifier obtaining the best performances is the RandomForest one with a precision equal to 0.886 and a recall of 0.899 for \(3+4\) [PERSON] score prediction, a precision equal to 0.803 and a recall of 0.873 for \(4+3\) Gleason score prediction and a precision equal to 0.888 and a recall of 0.879 for \(4+4\) Gleason score prediction. The model built with the C 4.5 algorithm obtains performances slightly worse than the RandomForest one, while the SVM and the Gaussian ones obtain lower values for the several metrics (for instance, a recall equal to 0.170 for the \(4+4\) class with the SVM and a precision of 0.508 for the \(4+3\) class prediction for the Gaussian). Below, we calibrate the model with the best classification performances i.e., the one exhibited by the RandomForest one. In general, the score obtained from a classifier (that outputs a number between 0 and 1) is not necessarily a well-calibrated probability. This is not always a problem because generally it is enough to obtain scores that correctly detect the instances, even if they do not actually correspond to real probabilities (for instance, it is not important that the built classifier predicts with 10% of probability of the class; it is enough that the class is rightly predicted). From the other side, the well-calibrated classifier--if it reports a score equal to 0.9 for an instance under analysis, this means that the instance would be true 90% of the time and false 10% of the time. Figure 4 shows the RandomForest uncalibrated classifier plot. The model was built with 25 base estimators (i.e., trees). The plot shows the probability vector. In particular, from the plot, it seems that the instances related to the \(3+4\), \(4+3\) and \(4+4\) Gleason scores fall into the corners (the red one for the \(4+3\) [PERSON] score, the green one for the \(3+4\) [PERSON] score and the blue one for the \(4+4\) [PERSON] score). Several \(4+4\) Gleason score instances appear in the plot (the blue arrows), but, in general, the remaining instances fall into their respective corners. If an unseen instance falls in the white space of the plot, the classifier is not able to make the prediction. The sigmoid Calibration, the one that we apply to calibrate the classifier, means to fit a Logistic Regression classifier using the (0 or 1) outputs from the original model [31]. The classifier is initially calibrated for each class separately in a one-vs.-rest way. When we make prediction probabilities for unknown data, the calibrated probabilities for each class are separately predicted [23]. Since these probabilities do not necessarily add up to one, post-elaboration is performed to normalize them. Figure 4: Uncalibrated classifier. Figure 5 illustrates how the calibration changes predicted probabilities for a \(3+4\), \(4+3\) and \(4+4\) Gleason score classification problem. The model shown in Figure 5 is the same as depicted in Figure 4, the only difference is that the second one was trained with the sigmoid [32]. As result, the calibrated plot shows that the probability vectors are moving from the edges towards the center. In this way, all the points of the plane into which never seen instances of the radiomic features can fall will have a prediction by the classifier.