## 8 Discussion  
(1) Aspects of the multicollinearity problem. As can be seen from Figure 8 and Table 6 of the modeling results after PCA treatment, the modeling effects of XGBoost, LightGBM, CatBoost, and RF decreased after PCA treatment of the indicator system, with the most significant decrease in CatBoost modeling effects. On the contrary, there was a very small improvement in the model effect of SVM and MLP. It is especially noteworthy that XGBoost, LightGBM, CatBoost, and RF are all tree models. In fact, tree models are good at capturing nonlinear relationships (e.g., interactions and segmentation functions) between features and targets [36], which may be destroyed by linear transformations of PCA. Meanwhile, the tree model itself can effectively deal with the multicollinearity problem [37]. Therefore, the PCA processing of the data before inputting them into XGBoost, LightGBM, CatBoost, and RF may rather reduce the model effect. The experimental results of this study verify this point of view as well. In addition, [PERSON] et al. [38] showed similar results in their experiments: the decision tree (DT) model R\({}^{2}\) was 0.872, while the principal component analysis-decision tree (PCA-DT) model R\({}^{2}\) was 0.849, and the model effect was worse after PCA treatment. DT also belongs to the tree model. It can be seen that tree models (XGBoost, LightGBM, CatBoost, and RF) inherently have excellent ability to deal with nonlinear relationships and multicollinearity problems, so there is often less need to consider the multicollinearity problem when using tree models for prediction tasks. In addition, for SVM and MLP, although the modeling effect is improved after PCA treatment, the improvement is very limited, with a maximum improvement of only 2.38%. This indicates that the multicollinearity problem of the original data is not serious. (2) Comparison of the performance of the models. As can be seen from Tables 7-14, in the I-I system, CatBoost had the highest average accuracy (0.6950), average precision (0.7106), average recall (0.6950), and average F1 score (0.6944), which was significantly better than the other models. In the I-R system, CatBoost also performed outstandingly, with the highest average accuracy (0.6913), average precision (0.7052), average recall (0.6913), and average F1 score (0.6907). In addition, CatBoost's stability was significantly better than other models, both in the I-I system and the I-R system. CatBoost's excellent performance may be attributed to its efficient processing of class features and its ability to resist overfitting, which can better capture nonlinear relationships in rockburst prediction. LightGBM's overall performance in the I-I and I-R systems was second only to CatBoost, with average accuracies of 0.6801 and 0.6863, respectively. It is also worth noting that LightGBM's training speed was significantly faster than that of the other models, which makes it suitable for real-world application scenarios that require fast responses. The average accuracy of XGBoost in the I-I and I-R systems was 0.6776 and 0.6751, respectively, which is a moderate but stable performance. RF performed well in the I-I system, with an average accuracy (0.6873) second only to CatBoost, but RF's performance in the I-R system was significantly degraded, with a more pronounced drop in performance in the low-dimensional system. SVM and MLP performed poorly in all the index systems. As can be seen from Figures 9-12, the performance indicators of SVM and MLP models in all aspects were significantly inferior to the other four models, especially in the I-R system, where the performance was even worse. (3) Comparisons across indicator systems. Under the I-I system, as can be seen in Tables 7-14, the average accuracy of all models decreased from 0.6632 to 0.6529 when decreasing from seven dimensions to fourdimensions, which is a relatively small decrease (about 1.5%).