## 1 Introduction
### Tree-Based Ensembles and Other Methods  
In addition to ANN and SVM, various tree-based machine learning methods have been applied to flyrock prediction, often yielding performance on par with the best ANN/SVM models. Decision tree ensembles like random forests and gradient boosting machines can naturally handle nonlinear interactions and have the advantage of built-in variable importance analysis. [PERSON] et al. [45] evaluated four tree-based models--decision tree (DT), random forest (RF), extreme gradient boosting (XGBoost), and adaptive boosting (AdaBoost)--for a mine dataset. All four techniques provided accurate predictions (R\({}^{2}\) > 0.95), with AdaBoost being the most precise (R\({}^{2}\)\(\approx\) 0.99 for both training and testing). Such near-perfect fits indicate that the models captured almost all variance in the data, though the authors cautioned that burden and spacing had the least impact on the model output while powder factor had the highest influence. [PERSON] et al. (2016) similarly found that a regression tree model outperformed a multiple linear regression for flyrock distance prediction in a Malaysian quarry, based on metrics like median absolute error and R\({}^{2}\). The regression tree was more precise, and a sensitivity check again pointed to powder factor as the dominant factor affecting flyrock throw. These results reinforce that ensemble or rule-based tree models can be highly effective. One advantage is that they are relatively straightforward to apply and interpret; for example, a regression tree yields if-then rules similar to expert reasoning (e.g., \"if stemming < X and charge > Y, expect flyrock > Z\"). Indeed, [PERSON] and [PERSON] (2015) proposed a novel classification approach using multiple discriminant analysis (MDA) to categorize flyrock throw severity in a quarry. Instead of predicting an exact distance, their model classifies blasts into risk categories (no flyrock, moderate flyrock, and severe flyrock) based on blast parameters, aligned with regulatory safety criteria. The MDA-based model successfully classified flyrock outcomes for test blasts and has the benefit of simplicity--it does not require specialized software or extensive training to use. The authors even produced a territorial map for the quarry so that engineers can easily determine the expected flyrock severity class from blast design parameters ([PERSON] and [PERSON], 2015). This approach, while not yielding a numeric prediction, is very practical for field use as a quick risk assessment tool. Ensemble learning has also been used in creative ways. [PERSON] et al. (2019) (as mentioned earlier) combined multiple SVRs and a GLM-net aggregator to exploit diverse models' strengths, achieving R\({}^{2}\) = 0.99-level accuracy. [PERSON] et al. (2017) took an ensemble of ANNs approach: they trained five different ANN models and then ensembled their predictions to train a meta-ANN (referred to as EANNs). This stacked model attained R\({}^{2}\)\(\approx\) 0.986 (with very low error, e.g., RMSE -4.3 m) on the flyrock dataset, outperforming any single ANN and even a benchmark ANN of identical structure. Such ensemble methods benefit from averaging out individual models' errors, often yielding more stable and accurate predictions. However, a potential downside is the complexity of implementation and the need for more data to train multiple models. In practice, these approaches show that combining models can push the predictive accuracy to extremely high levels--albeit with the caveat that models trained and tested on the same site's data (especially if limited in size) might overfit to that context. For example, an AdaBoost or EANN model achieving \(\sim\)99% accuracy on a given quarry's blasts ([PERSON] and [PERSON], 2015; 2015) may not maintain that level on a different mine without retraining. Recognizing this, some recent studies explicitly tested generalization: [PERSON] et al.