## 6 Classification Models  
Since the text dataset is converted to a multi-dimensional numeric dataset by computing the linguistic features of every text, it is now possible to adopt the most popular classification models and training algorithms available in the machine learning literature [39; 62]. In order to validate our approach for the classification of the complexity of an Italian text, we conducted an extensive experimental comparison by training and evaluating 10 classification models on the dataset previously described. The implementations provided in the popular Sci-kit Learn library [40] (version 0.23, the last stable release at the time of writing) were used in this work. Moreover, before training the classification models, the numeric dataset was normalized in order to bring the different features to a common and comparable scale, thus avoiding possible biases due to the different ranges of the different features. Hence, we have executed a standardization procedure independently on every feature dimension, i.e., every feature value \(x\) is transformed to \(\frac{x-m}{q_{1}-q_{1}}\), where \(m\), \(q_{1}\) and \(q_{3}\) are, respectively, the median, first, and third quartiles for the given feature on the considered dataset. This procedure is known to be robust to outliers [39] and it was chosen because we have observed some outlier values in few features of our numeric dataset. The 10 classification models considered in this work are listed in Table 2 and briefly described in the following together with their settings. For the parameters not mentioned in the descriptions, we have adopted the default values as set in the Sci-kit Learn library. The random forest (RF) [63] and gradient boosted decision tree (GBDT) [64] are two ensemble-based classification models that train multiple weak decision tree classifiers and compose their predictions. RF uses the so-called _bagging_ technique [39], while GBDT is based on the _boosting_ process [39]. Practically, RF trains multiple decision trees simultaneously, each one on a different random sample of the dataset, and then averages their predictions. Instead, GBDT sequentially trains a series of decision trees, each one on the residual error function of the previous tree, thus building an additive loss function that is minimized by means of a gradient descent algorithm. After some preliminary experiments (see also [29]), we used 100 weak decision tree estimators with a maximum depth equal to the integral part of the square root of the number of features (in our work: \(\lfloor\sqrt{139}\rfloor=11\)). The support vector machine (SVM) model [65] aims at constructing a set of hyperplanes in a high-dimensional space in order to separate the regions of the space corresponding to sample instances from the different classes (i.e., the CEFR levels in our case). A higher dimensional space is implicitly induced by a non-linear kernel function that, in our case, is the commonly adopted radial basis function. Further parameters that weigh the regularization penalty and the influence of the training instances on the decision surface are, respectively, \(C\) and \(\gamma\) that, in our preliminary work [30], have been experimentally tuned to \(C=2.24\) and \(\gamma=0.02\). The multi-layer perceptron (MLP) [62] is the classical feed-forward neural network, which is a prediction model organized in different layers of so-called artificial neurons: the first--or input--layer is formed by the 139 numeric features considered in our work, the last--or output--layer produces an estimated output value for every one of the four target classes considered (i.e., the CEFR levels), while one or more inner--or hidden--layers allow us to learn a mapping from the input to the output. Any artificial neuron is connected to all the neurons in the previous layer, all the connections have a weight, and the output of a neuron is a non-linear combination of its weighted input values.