## 4 Discussion and Results
Various validation methods can be utilised, such as holdback, K-fold, and the incorporation of a validation column. To facilitate the development of a model, a series of steps are taken. The model parameters are subjected to a penalty, and the penalties imposed on these parameters are optimised using the validation set. The validation method is chosen as a random holdback, which means that the original data is divided into training and validation sets in a random manner, and the proportion of the original dataset to be allocated as the validation set, often known as the holdback. The process of random selection in this study is grounded in the principles of stratified sampling, which involves dividing the model factors into distinct strata. This approach aims to provide training and validation sets that exhibit a higher degree of balance compared to those obtained through simple random sampling. Figure 6 displays plots that compare the actual values with the predicted values for the training and validation procedures. The plots use the bootstrap forest method shown in red, the boosted tree method represented in green, and the neural boosted method represented in blue. The data points exhibit a strong correlation with the line, suggesting a high degree of relationship between the anticipated values and the actual values. Boosting refers to the procedure of constructing a substantial neural network model by training a series of smaller models. Each of the smaller models is fitted using the scaled residuals of the preceding model. The models are aggregated to create the overarching final model. The technique employs validation to determine the appropriate number of component models to fit, ensuring that it does not exceed the set limit. Boosting often exhibits faster computational speed compared to training a single, big model. Nevertheless, the fundamental model needs to consist of a single layer with 1 to 2 nodes. The advantage of quicker fitting might be negated if a substantial quantity of models is supplied. Learning rates approaching 1 lead to quicker convergence on a final model but also have a greater inclination to overfit data. In order to address the issue of neural networks being prone to overfitting, the fitting procedure includes a penalty on the probability. The penalty term is represented as \(\lambda p(\beta i)\), where \(\lambda\) represents the regularisation parameter, and \(p(\;)\) denotes the penalty function, which is a function of the estimated parameters. The utilisation of the validation method is employed in order to ascertain the optimal value for the penalty parameter. Table 3 provides an overview of several penalty techniques. Figure 6: Illustration of the prediction outcomes and their accompanying metrics, which include the bootstrap forest, boosted tree, and neural boosted network. **(left)** Process of training. **(right)** The validation process. The authors of this research article conduct a comparative analysis between the proposed methodology and established prediction approaches, such as K Nearest Neighbours (kNNs) and boosted tree. The neural boosted model has outstanding performance, as shown by its consistently high training RSquare values throughout several folds and its higher validation RASE score. The mean validation RSquare for neural boosted is 0.9968, and the mean RASE for neural boosted is 1.2711. The elapsed time data indicates that the neural boosted models exhibited the longest duration for fitting. Table 4 displays the comprehensive comparison of forecast outcomes in relation to various methods. Each of the training, validation, and test sets is provided with a range of prognostic measures. The prognostic measures vary based on whether the response is categorical or continuous. For continuous response scenarios, the cross-validation statistics consist of a generalised R\({}^{2}\), an entropy R\({}^{2}\), the (negative) loglikelihood, the root mean squared error (RMSE), and the mean absolute deviation.