## 2 Contributions of the Paper  
The contributions of the proposed work are as follows. We remark here that the three contributions listed above meet the three dimensions outlined in the previous section (\(\mathcal{D}1\), \(\mathcal{D}2\), and \(\mathcal{D}3\)). Figure 2: This executive diagram summarizes the key components of the methods proposed in this paper. We start with the COVID-19 image data. With a small rolling window defined, we execute the backward dropping algorithm to select the important features within this window. For example, the rolling window may cover 4 variables, \(\{X_{1},X_{2},X_{3},X_{4}\}\), and the BDA could select \(\{X_{1},X_{2}\}\) as a variable module. Then, we can construct a new variable using the interaction-based feature engineer technique (see the construction of \(X^{\ddagger}\) in Equation (6) to appreciate this new design). In other words, using the selected variables \(X_{1}\) and \(X_{2}\), we construct \(X^{\ddagger}\). The procedure of the BDA is illustrated in the bottom left corner of the figure (we use a \(2\times 2\) window for simplicity). We set the starting point to be 12 (i.e., start from the pixel in the 12 th row and the 12 th column). From the data (size of \(128\times 128\)) to the 1 st layer (\(58\times 58\)), this gives us a new dimension that is computed by \(\lfloor(128-12-2+1)/2+1\rceil=58\) (see Equation (18)). We can repeat the process in the 2 nd layer and the 3 rd layer. After the 3 rd layer, we shrink the dimension to \(14\times 14\) (which gives us 196 new variable modules, i.e., the new \(X^{\ddagger}\)). We fully connect these 196 variable modules with the 10 neurons in the hidden layer (in practice, the number of hidden layers and the number neurons are tuning parameters). This novel design is fundamentally different than the conventional practice of using pretrained filters because it proposes to use an explainable measure, the I-score, to extract and build information directly from images in the training data. For each local variable (in the data, this refers to pixels; in the layers, it is referred to as variables), we compute the I-score values and the AUC (see Section 4.4 for a detailed discussion of AUC values) for that variable (using this variable as a predictor alone). We observe that the I-score value fully represents the predictivity of each local variable, which can be confirmed by the variable’s AUC value. The color spectrum of both the I-score and AUC are presented in the bottom part of the diagram. We observe I-score values exhibiting behavior parallel to AUC values. This means the variables with high I-score values have high AUC values, which indicates strong predictive power for the information in that location. This design heavily relies on the I-score and has an architecture that is interpretable at each location of the image at each convolutional layer. More importantly, the proposed design satisfies all three dimensions (\(\mathcal{D}1\), \(\mathcal{D}2\), and \(\mathcal{D}3\) in the Introduction) of the definition of interpretability and explainability. First, we introduce a model-free and interaction-based learning methodology, the influence score (I-score). We illustrate how to use the I-score to select and measure features that are directly linked to the predictivity of the response variable [21; 26]. Moreover, this quantifiable measure does not rely on any specification of the underlying model. Hence, this meets the first and the third requirements, i.e., \(\mathcal{D}1\) and \(\mathcal{D}3\) of interpretability and explainability. We apply this measure along with a greedy search algorithm called the backward dropping algorithm (see Section 3.2 for a detailed discussion to appreciate this method) locally to image data. In other words, instead of using a set of predefined filters (or kernel) that are applicable to various kinds of deep CNNs on image data by trial and error, we propose using the I-score and the backward dropping algorithm on a local window to extract important and influential features from image data.