## 2 Methods and Materials
### Learning Techniques  
In this work, a detailed analysis of a significant number of statistical learning methods has been proposed and more specifically in contrast with the efforts presented in the companion paper, in this case non-linear methods. The application of this type of methods requires the fulfillment of a certain process generally known as learning technique. These techniques mostly are either supervised or unsupervised approaches. Supervised ML algorithms collect a series of input data (predictor variables) and output responses (labels), and with this information, the model is trained to generated reasonable predictions [19]. On the other hand, unsupervised learning algorithms search for similarity patterns of input data, without the need to give the algorithm any output or response data. Supervised approaches are subdivided into classification and regression methods. Classification is used to predict discrete responses while regression is used to predict continuous outputs. Regression techniques can be subdivided mostly in two types, namely parametric and non-parametric algorithms. The former try to adjust the response of the model by means of a function that represents the relation between input variables and output, whereas the latter try to adjust complex regressions whose relationships among variables are not defined by a given functional form [20; 21].  
In our specific case, as the goal is to build a model that follows a certain continuous response, in order to characterize the aimed company valuation, it will be very well represented if we consider it from an arithmetical stand point as regression type process. Therefore, mathematically we can outline as a non-parametric and supervised method that describes a continuous variable (\(y\)) in terms of a \(m\) samples, each of them characterized by \(d\) features. Therefore, we denote the dataset as \(\{(\mathbf{x}_{i},y_{i})_{i=1}^{m}\}\), with \(\mathbf{x}_{i}=[x_{n,1},x_{n,2},\cdots,x_{n,d}]\).  
The dataset was divided into two independent subsets for achieving generalization capabilities [22]. We used the 70% of the samples as training set to build the model, whereas the remaining 30% were used to evaluate the performance of the model. This process was repeated 100 times to avoid bias and to characterize statistically the dataset, so that we considered 100 different training and test realizations. The performance of the models was evaluated in terms of mean and Standard Deviation (STD) of the following merit figures: Mean Absolute Error (MAE), which is calculated as the mean absolute error between the predictions \(\widehat{y}\) and the real value \(y\) (see Equation (12) in the companion paper); Mean Squared Error (MSE), which measures the mean squared error and offers a more meaningful description of the results (see Equation (13) in the companion paper); Root Mean Square Error (RMSE), obtained as the square root of MSE (see Equation (14) in the companion paper); and \(D\)-index of agreement [23; 24], which varies from 0 to 1 with higher values indicating better performance, and it is obtained as  
\[D=1-\frac{\sum_{i=1}^{m}(\widehat{y}_{i}-y_{i})^{2}}{\sum_{i=1}^{m}(|\widehat {y}_{i}-\overline{y}|+|y_{i}-\overline{y}|)^{2}} \tag{1}\]Different ML algorithms were benchmarked. In order to quantify and measure the generalization error of the different models and to select those ones with lower bias, a cross-validation strategy was considered. Although there are different techniques for this purpose, we followed a _K-fold_ cross-validation strategy, which takes a dataset and divides it into \(K\) subsets. One of the subsets is used as test data and the rest (_K_\(-\)_1_) as training data. The cross-validation process is repeated for \(k\) iterations with each of the possible subsets of validation data [25]. Before starting the learning process, each feature is standardized and centered, in order to have zero mean and unit STD.