## 3 Methodology
### Selection of Predictors  
Once the training dataset was prepared, relevant variables were selected, i.e., those that have a true relationship with the output to be predicted. The use of too many variables would add noise to the models. Among the different existing variable selection methods, the wrapper methods were used. These methods search for a subset within the dataset that determines the optimal combination of variables, which allows for the best possible performance in predicting the target variable [42]. This present study incorporates variable selection algorithms based on the use of random forests, bootstrap averaging, decision trees, and gradient boosting. In particular, the following methods were used: (i) stepwise forward and backward selection, (ii) Boruta selection model, (iii) recursive feature elimination, (iv) simulated annealing, and (v) genetic algorithms. Machine learning methods based on decision trees were first described in [43]. These methods learn from the number of times an event occurs compared to another, without considering the order of occurrence of these events. The results are shown in the form of a probability tree. These algorithms are widely used in machine learning techniques, particularly in variable pre-selection, as they have low predictive potential but a high capacity for searching for rules and interactions between variables, particularly categorical variables (since they trace nonlinear relationships very well). One advantage of these pre-selection methods is that they do not assume any theory about the data and properly and efficiently handle the missing data [44]. In addition, decision trees are the basis of other algorithms that have predictive capability, such as bagging, random forest, and gradient boosting. The precursor of the technique called bagging [45] uses the advantages of decision trees to avoid their predictive instability, thus creating a variable selection technique called  
Figure 3: Map of the study area with the location of the 3106 seismic-induced slope instability samples (orange dots) and 3106 stable site samples (green dots). bootstrap averaging. It is based on generating multiple versions of a predictor to obtain an aggregated version, which is used to predict the variable and is the starting point in the next step. It obtains a decrease in variance based on the average of previous estimates. Gradient boosting, proposed by the authors in [46], is based on updating the decrease direction given by the negative gradient of the error function. These algorithms are extremely versatile and are easy to implement and monitor. They have a high predictive capacity and are robust against irrelevant variables, but they are not suitable for problems with low complexity [44]. Among the variable selection algorithms used in this study, stepwise selection methods are based on variable selection using stepwise regression. This method is a hybrid between forward and backward stepwise selections [47]. Forward stepwise selection starts with a model that does not contain any variable, known as the null model. Then, it begins to add significant variables in terms of \(p\)-value or lower values in the RSS (residual sum of squares) model sequentially until a specified stopping rule is reached or until all considered variables are included in the model. The stopping rule is usually defined based on a certain \(p\)-value threshold, and if the threshold is exceeded, the variable is added to the model. The \(p\)-value sensitivity threshold can be defined either fixedly or using AIC (Akaike information criterion) or BIC (Bayesian information criterion). The problem with defining the threshold following these criteria is that the threshold changes for each variable. Backward stepwise selection begins with a full model of variables, which are removed one by one based on a stopping criterion [48]. This selection method allows variables to be selected following a simple and easily interpretable statistical model.