## 4 Results  
This section presents and discusses the achieved experimental results. The best performing configuration of each architecture is shown in Table 5. These results suggest that the choice of the parameters is strictly related to the considered architecture, and it is something that must be taken into account before tackling the PCa classification problem. Table 6 reports the average values of loss and AUROC on the training and test sets, allowing for a comparative analysis of the different architectures considered in this study. According to these results, AlexNet is the best architecture when considering the values of the loss function on the training instances, but it severely overfits the training data, as shown when considering the test set. On the training set, the second-best performer is XmasNet-CRFpp, but also for this architecture a severe amount of overfitting can be noticed when one focuses on the loss function on \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Architecture** & **Loss Train** & **Loss Test** & **AUROC Train** & **AUROC Test** \\ \hline XmasNet & 0.500 \(\pm\) (0.023) & 0.540 \(\pm\) (0.043) & 0.622 \(\pm\) (0.054) & 0.517 \(\pm\) (0.101) \\ AlexNet & 0.096 \(\pm\) (0.032) & 0.537 \(\pm\) (0.023) & 1.000 \(\pm\) (0.000) & 0.588 \(\pm\) (0.051) \\ VGG16 & 0.474 \(\pm\) (0.021) & 0.481 \(\pm\) (0.018) & 0.729 \(\pm\) (0.047) & 0.707 \(\pm\) (0.050) \\ ResNet & 0.496 \(\pm\) (0.020) & 0.528 \(\pm\) (0.023) & 0.658 \(\pm\) (0.065) & 0.520 \(\pm\) (0.100) \\ XmasNet-CRFpp & 0.433 \(\pm\) (0.082) & 0.730 \(\pm\) (0.242) & 0.796 \(\pm\) (0.069) & 0.388 \(\pm\) (0.303) \\ CRF-XmasNet & 0.507 \(\pm\) (0.077) & 0.566 \(\pm\) (0.097) & 0.695 \(\pm\) (0.126) & 0.573 \(\pm\) (0.191) \\ CRF-AlexNet & 1.150 \(\pm\) (0.366) & 1.260 \(\pm\) (0.392) & 0.536 \(\pm\) (0.191) & 0.598 \(\pm\) (0.169) \\ CRF-VGG16 & 0.644 \(\pm\) (0.267) & 0.732 \(\pm\) (0.206) & 0.796 \(\pm\) (0.209) & 0.615 \(\pm\) (0.147) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Loss and AUROC values for each architecture. The average value (with standard deviation in parenthesis), obtained over 30 independent runs is shown. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Values** \\ \hline Optimizer & \{SGD, Adam, RMSPROP\} \\ Learning rate (\(l_{r}\)) & \{\(1\times 10^{-1},\ 1\times 10^{-2},\ 1\times 10^{-3}\ 1\times 10^{-4},\ 1\times 10^{-5},\ 1\times 10^{-6},\ 1 \times 10^{-7}\)\} \\ Momentum (\(m\)) & \{0.0, 0.9, 0.99, 0.999\} \\ Decay (\(d\)) & \{0.0, 0.1, 0.01, 0.001\} \\ Nesterov (\(n\)) & \{0, 1\} \\ Amsgrad (\(a\)) & \{0, 1\} \\ CRF \(\theta_{a}\) & \{0.5, 1, 2, 3\} \\ CRF \(\theta_{\beta}\) & \{0.5, 1, 2, 3\} \\ CRF \(\theta_{\gamma}\) & \{0.5, 1, 2, 3\} \\ \hline \hline \end{tabular}
\end{table} 
Table 4: List of the hyper-parameters considered in the grid search. \begin{table}
\begin{tabular}{l l c c c c c c} \hline \hline
**Architecture** & **Optimizer** & \(l_{r}\) & \(m\) & \(d\) & \(n\) & \(a\) & \(\theta_{a}\) & \(\theta_{\beta}\) & \(\theta_{\gamma}\) \\ \hline XmasNet & RMSPROP & \(1\times 10^{-5}\) & NA & 0 & NA & NA & NA & NA & NA \\ AlexNet & RMSPROP & \(1\times 10^{-5}\) & NA & 0 & NA & NA & NA & NA \\ VGG16 & Adam & \(1\times 10^{-4}\) & 0.999 & 0 & 0 & NA & NA & NA \\ ResNet & Adam & \(1\times 10^{-5}\) & 0.99 & 0 & 0 & NA & NA & NA \\ XmasNet-CRFpp & RMSPROP & \(1\times 10^{-5}\) & NA & 0 & NA & NA & 1 & 1 & 0.5 \\ CRF-XmasNet & RMSPROP & \(1\times 10^{-4}\) & 0.99 & 0.1 & NA & NA & 1 & 1 & 0.5 \\ CRF-AlexNet & RMSPROP & \(1\times 10^{-3}\) & 0.99 & 0.01 & NA & NA & 2 & 3 & 2 \\ CRF-VGG16 & RMSPROP & \(1\times 10^{-4}\) & 0 & 0 & NA & NA & 2 & 2 & 3 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Best performing configuration of each architecture. NA denotes Not Applicable. the test set. Still considering the training set, the third-best performer is VGG16, which also produces the lowest (i.e., the best) average loss function value on the test set.