## 4 Results and Discussion
The underlying distribution of the models has been estimated using a smooth kernel density function by showing attractive benchmark points, namely the median and quartiles depicted in Figure 8. It is abundantly clear that KStar and BRT have closer Q25% values (11.366 and 11.562, respectively) to the observed values (11.395) compared with the LWLR and LGP approaches, whereas the LGP and LWLR Q75% values (13.251 and 13.146, respectively) exhibit better agreement with the observed values (13.21). Given the arrangement of the datasets, it is evident that the first Q25% is filled into the training data. Regarding KStar, the remarkable performance in training and disappointment in the testing phase implies that overfitting occurred in this paradigm. The trend variation of BI plots in both training and testing modes is shown in Figure 9. The results indicate that the LGP model can properly capture the nonlinear behavior of BI in both triaging and testing datasets, and is capable of demonstrating promising predictive performance compared to other models. Complete error analysis was performed to evaluate the performance of the proposed predictive methods in BI estimation. According to Figure 10, the KStar (RDB = 5.52%) and LWLR (RDB = 21.51%) models are identified as having the best and worst predictive performance, as indicated from the lowest and highest relative deviation bands in the training stage, respectively. Furthermore, LGP with the lowest RDB (14.40%) and KStar with the highest RDB (23.41%) have yielded the most promising and weakest results in forecasting BI in testing mode, respectively. Figure 7: Comparison of four soft computing approaches and observed BI using scatter plot. As a final error assessment, the cumulative distribution function (CDF) of the absolute percentage of relative error (APRE) for the testing dataset was considered. Figure 11 indicates that for more than 80% of testing datasets in predicting BI values, the APRE values of LGP, BRT, LWLR, and KStar are less than 5%, 7.01%, 7.65%, and 7.80%, respectively. Eventually, it can be inferred that the LGP model, as the main novelty of this research, is superior to all proposed AI models for accurately predicting BI. The KStar approach, despite its amazing performance in the training phase, yielded the weakest results in the test phase among all models, which means that this method may not work properly for unseen data. The KStar model cannot be identified as an efficient predictive method for BI prediction due to overfitting. Thus, LGP and LWLR were identified as the best and second-best predictive models. The BRT model--ranking third, with predictive performance close to LWLR--yielded the admitted results for the prediction of BI values. It is worth noting that although KStar in this study showed unfavorable performance in testing mode, the accuracy of its results is far better than the results of previous research [3]. In the literature, some studies have predicted BI by using different machine learning methods. [PERSON] et al. [69] used the genetic algorithm (GA) and particle swarm optimization (PSO) to predict BI. According to their results, the values of R\({}^{2}\) ranged between 0.851 and 0.932. In another study, [PERSON] et al. [25] predicted BI through a combination of ANN and firefly algorithm, yielding prediction results with an R\({}^{2}\) of 0.896. In the present study, BI has been predicted with better performance (R\({}^{2}\) of 0.953) from the LGP model. This indicates the effectiveness of the model proposed in this study compared to aforementioned models  
Figure 8: Performance assessment of predicted and observed BI values using half violin plots. used in the literature. According to the objectives of this study, the uncertainty of the data has not been investigated. Given great importance, uncertainty of data and results of machine learning-based methods could be considered as the subject of future research. Also, the models presented in the current study generally suffer from a lack of laboratory data.