## 5 Experiment Results and Performance Evaluation  
### Predictive Models and Performance Metrics  
The architectures and hyperparameters of the CNN and LSTM models used in our experiment are summarized in Table 4. The global model parameters consist of configurations for two neural network architectures: Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM). For the CNN, the input dimension is set to 30, indicating the size of input features, while the hidden dimension is also 30, determining the number of filters in the convolutional layers. No specific number of layers is specified for the CNN. The learning rate for optimization is set at 0.001, determining the step size during parameter updates, and the training is conducted for 10 epochs with a batch size of 64 samples. The log interval parameter defines the frequency at which the training progress is logged, set to every 10 batches. For the LSTM model, the input and hidden dimensions are both set to 30, specifying the size of input features and the numbers of hidden units in the LSTM layers, respectively. One layer of LSTM is employed in this configuration. Similarly, the learning rate, number of epochs, batch size, log interval, and splitting ratio remain consistent with the CNN settings. Additionally, the data splitting ratio is set at 70:30, indicating the proportion of data allocated for training and testing/validation, respectively. The model operates across three separate banks, possibly denoting different data sources or subsets utilized in the federated learning framework. ADAM, SGD, and MSGD deep learning optimizers are utilized to improve network weights based on gradients and other models' information during the training process, to ensure our predictions are as accurate and optimized as possible. Adaptive Moment Estimation (ADAM) is a popular deep optimizer algorithm for training deep learning models. It combines the ideas of RMSProp and Momentum, computing adaptive learning rates for each parameter [71] as follows:  
\[ \begin{split} m_{t}&=\beta_{1}\cdot m_{t-1}+(1-\beta _{1})\cdot g_{t},\\ v_{t}&=\beta_{2}\cdot v_{t-1}+(1-\beta_{2})\cdot g_{t }^{2},\\ \hat{m}_{t}&=\frac{m_{t}}{1-\beta_{1}^{t}},\\ \hat{o}_{t}&=\frac{v_{t}}{1-\beta_{2}^{t}},\\ \theta_{t+1}&=\theta_{t}-\frac{\eta}{\sqrt{\hat{o}_{t }}+\epsilon}\cdot\hat{m}_{t},\end{split}  \tag{1}\]  
where  
* \(m_{t}\) and \(v_{t}\): first and second moment estimates. * \(g_{t}\): gradient at time step \(t\). * \(\beta_{1}\) and \(\beta_{2}\): decay rates for first and second moment estimates
* \(\eta\): learning rate. * \(\epsilon\): small constant added to the denominator to prevent division by zero. Stochastic Gradient Descent (SGD) uses a randomly selected single sample for each iteration [72]. \[\theta_{t+1}=\theta_{t}-\eta\cdot\
abla J(\theta_{t}), \tag{2}\]  
where  
* \(\theta_{t}\): parameter vector at time step \(t\). * \(\eta\): learning rate. * \(\
abla J(\theta_{t})\): gradient of loss function \(J\) with respect to parameters \(\theta_{t}\). Mini-batch Stochastic Gradient Descent (MSGD) updates the parameters using mini-batches of data, providing a balance between the efficiency of SGD and the stability of batch gradient descent [73]. \[\theta_{t+1}=\theta_{t}-\eta\cdot\frac{1}{m}\sum_{i=1}^{m}\
abla J(\theta_{t}; x_{i},y_{i}), \tag{3}\]  
where  
* \(\theta_{t}\): parameter vector at time step \(t\). \begin{table}
\begin{tabular}{c c c} \hline \hline  & \multicolumn{2}{c}{**Model**} \\ \hline
**Parameter** & **CNN** & **LSTM** \\ \hline Input\_dim & 30 & 30 \\ Hidden\_dim & 30 & 30 \\ Num\_layers & 0 & 1 \\ Learning\_rate & 0.001 & 0.01 \\ Num\_epochs & 10 & 10 \\ Batch\_size & 64 & 64 \\ Log\_interval & 10 & 10 \\ Splitting\_ratio & 70:30 & 70:30 \\ Num\_banks & 3 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Architecture of the CNN and LSTM models. * \(\eta\):learning rate. * \(m\): mini-batch size.