## 2 Data Collection
### Loss Function  
The loss function serves as a metric for assessing the adequacy of a model in terms of its capability and proficiency in predicting new values. When training a machine learning model, the objective is to identify a point where the loss function is minimized. One common approach to finding the minimum of the loss function involves utilizing derivatives and the \"Gradient Descent\" algorithm. A machine learning algorithm systematically refines a model's parameters through iterative processes, guided by the evaluation of a loss function. Among the widely employed loss functions, LMSE and LMAE exhibit distinctive characteristics. The loss function of Mean Square Error (MSE), abbreviated as LMSE, calculates the average of the squared differences between the predicted and actual values. The loss function of Mean Absolute Error (MAE), abbreviated as MAE, utilizes the absolute difference between the predicted and actual values as a criterion, similar to MSE. However,it disregards the direction of this difference [54]. Therefore, in the computation of the error in MAE, only the magnitude of the difference is considered. LMSE and LMAE are defined as:  
\[L_{MSE}=\frac{1}{n}{\sum\limits_{i=1}^{n}(y_{i}-\hat{y}_{i})^{2}} \tag{18}\]  
\[L_{MAE}=\frac{1}{n}{\sum\limits_{i=1}^{n}}|y_{i}-\hat{y}_{i}| \tag{19}\]  
where \(n\) is the number of observations, \(y_{i}\) is the actual value for observation \(I\), and \(\hat{y}_{i}\) is the predicted value for observation. The LMSE is notable for expediting convergence under its diminishing gradient. However, it possesses a tendency to penalize outliers, compelling predictions towards mean values. Consequently, LMSE may exhibit limitations in capturing pronounced disturbances within authentic observations. On the other hand, LMAE constitutes a linear scoring methodology. Relative to LMSE, LMAE demonstrates enhanced resilience in the presence of outliers and excels in replicating observations situated significantly distant from mean values [55]. The Huber Loss function (L\({}_{8}\)), also known as Smooth Mean Absolute Error, and the Logarithm of Hyperbolic Cosine Loss function (L\({}_{\text{log-cosh}}\)), have been employed in this study. The L\({}_{8}\) is less sensitive to outliers compared to LMSE. Additionally, unlike the LMAE loss function, it is differentiable, allowing for ease in its minimization. The calculation method for the L\({}_{8}\) is expressed by the following equation:  
\[L_{\delta}=\left\{ \begin{array}{ll}\frac{1}{N}{\sum\limits_{i=1}^{N}}\;w_{i }\cdot\frac{1}{2}(y_{i}-\hat{y}_{i})^{2}&|y_{i}-\hat{y}_{i}|\leq\delta\\ \frac{1}{N}{\sum\limits_{i=1}^{N}}\;w_{i}\cdot\left(\delta|y_{i}-\hat{y}_{i}|- \frac{1}{2}\delta^{2}\right)&|y_{i}-\hat{y}_{i}|>\delta\end{array} \right. \tag{20}\]  
The L\({}_{8}\) provides a compromise between the LMSE and LMAE, exhibiting reduced sensitivity to outliers while maintaining differentiability for optimization purposes. When \(\delta\) tends to zero, the L\({}_{8}\) approaches the LMSE, and, when \(\delta\) approaches a large value, it converges to the LMAE. The application of the L\({}_{8}\) results in a scenario where, as the error decreases, its derivative decreases, simplifying the minimization of the L\({}_{\delta}\). Consequently, this loss function diminishes the influence of outliers in calculations when outliers are present in the data. Additionally, as the error decreases, the minimization of the L\({}_{8}\) becomes easily attainable [56]. Another loss function particularly employed in regression is the L\({}_{\text{log-cosh}}\). To compute L\({}_{\text{log-cosh}}\), it suffices to take the logarithm of the hyperbolic cosine of the error between the predicted and actual response variables.