## 4 Results and Discussion  
### Performance Evaluation of Customized CNNs  
Figure 7 shows the optimized architecture and parameters of the sequential CNN, obtained through Bayesian learning. We performed 100 objective function evaluations toward optimizing the model parameters. The optimized values are found to be 6, 1 \(\times\) 10\({}^{-3}\), 0.9, and 1 \(\times\) 10\({}^{-6}\) for the network depth, learning rate, momentum, and L2-regularization parameters respectively. The number of convolutional layer filters is increased by a factor of 2 each time a max-pooling layer is used, in order to ensure roughly the same number of computations in the network layers. Rectified Linear Unit (ReLU) layers are added to introduce non-linearity and prevent vanishing gradients during backpropagation [7]. Our analysis shows an increase in the performance of the residual and inception CNNs when the number of filters in the convolutional layers of the succeeding blocks are increased by a factor of 2. We found the optimal hyperparameter values for the residual, inception, and VGG16 models through a randomized grid search. The values are tabulated in Table 2.  
The customized CNNs are evaluated with the baseline and cropped ROI data. The results are tabulated in Table 3. We observed that the performance of the models with the cropped ROI is relatively promising in comparison to the baseline in classifying normal and pneumonia infected CXRs. This is obvious because the models trained with the cropped ROI learn relevant feature representations toward classifying the task of interest. Figure 7: The optimized architecture of customized sequential CNN. The customized VGG16 model demonstrates promising performance than the other CNNs under study. The model learned generic image features from ImageNet that served as a good initialization compared to random weights and trained end-to-end on the current tasks to learn task-specific features. This results in faster convergence with reduced bias, overfitting, and improved generalization. In classifying bacterial and viral pneumonia, no significant difference in performance is observed for the customized VGG16 model with the baseline and cropped ROI. In the multi-class classification task, the cropped ROI gave better results than the baseline data. However, we observed that the differences in performance are not significant. This may be due to the reason that the dataset under study already appeared as cropped, and the boundary detection algorithm resulted in a few under-segmented regions near the costophrenic angle. The customized sequential, residual, and inception CNNs with random weight initializations didn't have the opportunity to learn discriminative features, owing to the sparse availability and imbalanced distribution of training data across the expected classes. We observed that the sequential CNN outperformed the residual and inception counterparts across the classification tasks. The usage of residual connections is beneficial in resolving the issue of representational bottlenecks and vanishing gradients in deep models. The CNNs used in this study have a shallow architecture. The residual connections did not introduce significant gains into the performance for the tasks of interest. Unlike ImageNet, the variability in the pediatric CXR data is several orders of magnitude smaller. The architecture of residual and inception CNNs are progressively more complex and did not seem to be a fitting tool to use for the tasks of interest. The confusion matrices \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Model** & **Learning Rate** & **Momentum** & **L2 Regularization** \\ \hline Residual CNN & \(1\times 10^{-3}\) & 0.9 & \(1\times 10^{-6}\) \\ Inception CNN & \(1\times 10^{-2}\) & 0.95 & \(1\times 10^{-4}\) \\ Customized VGG16 & \(1\times 10^{-4}\) & 0.99 & \(1\times 10^{-6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimal values for the hyperparameters of the customized residual and inception CNNs obtained through a randomized grid search.