## 4 Application
### Performance: Proposed Models and AUC Values  
This subsection presents the experimental results. A brief summary of a comparison of the conventional methods in the literature with the proposed method is presented in  
Figure 7: Two paths of ROC curves: ROC1 and ROC2. For each ROC curve, we can compute the AUC value. From ROC1, we can compute AUC1. From ROC2, we can compute AUC2. The mistake discussed in this section is reflected by a reduction in AUC values from path 1 to path 2. Table 9. A detailed report of the proposed methodology is presented in Table 10. We also plot the AUC values for the proposed models in Figure 8.  
Table 9 shows results of previous work on this data set. [PERSON] et al. [31] used a 50-layer CNN, ResNet50, and achieved an AUC value of 99%. They also proposed SqueezeNet, which delivered an even higher performance at 99.2% [31]. This near-perfect performance is largely due to the design of the convolutional layers and fine tuning. Their work shows that modern-day AI technology such as deep CNNs can perform the initial screening of patients infected by COVID-19 with a single scan of an image, which could reduce the workload of radiologists in practice. However, the number of parameters still far exceeds what humans can interpret. Moreover, it is unclear how these conventional methodologies can satisfy the three criteria (\(\mathcal{D}1\), \(\mathcal{D}2\), and \(\mathcal{D}3\)) of the definition of interpretable measures introduced in Section 1 in this paper. We read the experimental results of the proposed model in the following order. As stated in Section 3.3, the proposed architecture can be designed as deep or wide as desired by the user. All models start with 128 by 128 input images. In other words, the input data has \(128\times 128=16,384\) pixels. For simplicity of notation, let us denote \(\triangle\) as the set of parameters with the starting point of six, window size of \(2\times 2\), and a stride level of two. Let us further denote \(\square\) as the collection of parameters of starting point of on, window size of \(2\times 2\), and a stride level of two. Figure 8: The AUC path for all six models in the proposed work. These models are listed in Table 10 with detailed information including the parameters from each layer and the out-of-sample prediction performance. \begin{table}
\begin{tabular}{l l c} \hline \hline
**Previous Work** & **Number of Param.** & **AUC** \\ \hline DenseNet161 [31] & 0.8–40 M param. & 97.6\% \\ ResNet18 [31] & 11 M param. & 98.9\% \\ ResNet50 [31] & 25 M param. & 99.0\% \\ SqueezeNet [31] & \(\sim\)1.2 M param. * & 99.2\% \\ Average & \(>\)25 M & 97–99.2\% \\ \hline \multirow{3}{*}{Proposed Methods} & Average 100,000 param. & \multirow{3}{*}{98.3–99.8\%} \\  & (a 99\% reduction in no. of param.) & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: The experimental results on the COVID-19 data set from the literature. A number of different ultra-deep CNNs were used to classify COVID patients from non-COVID people. The performance is summarized below. * [PERSON] et al.disclosed that SqueezeNet has approximately 50 times fewer parameters than AlexNet. The proposed architecture achieves AUC values ranging from 98% to 99.8%. For details, please refer to Figure 8 and Table 10. The average number of parameters of the ultra-deep CNNs can exceed 25 million parameters with a top AUC value of 99.2%. The proposed method has an average number of parameters of less than 100,000 with a top AUC value of 99.8%. This is a 99% reduction in th number of parameters without sacrificing prediction performance. **Model 1. ** This model starts with input images that are sized \(128\times 128\). Using the parameter in set \(\triangle\), we create the first interaction-based convolutional layer (i.e., 1 st Conv. Layer in Table 10). This new matrix has dimension \(\lfloor(128-6-2+1)/2+1\rfloor\times\lfloor(128-6-2+1)/2+1\rfloor=61\times 61=3721\). These 3721 variables are directly used to create the output layer with two units (assuming using SoftMax as the loss function).