## 5 Conclusions  
**Explainable AI System for Early COVID-19 Screening. ** As the most important contribution of this paper, an explainable artificial intelligence (XAI) system is proposed to assist radiologists in the initial screening of COVID-19 and other related diseases using chest X-ray images for treatment and disease control. This innovation can revolutionize the application of AI systems in hospitals and healthcare systems. We anticipate that other related diseases with viral pneumonia signs can use the same detection methods proposed in our paper, which ensure the development of testing procedures with accountability, responsibility, and transparency for human users and patients. **A Heuristic and Theoretical Framework of XAI. ** This paper introduced a heuristic and theoretical framework for addressing the XAI problems in large-scale and high-dimensional data sets. We provided three criteria as necessary conditions and premises for a measure to be regarded as explainable and interpretable. The first dimension, \(\mathcal{D}1\), states that an interpretable measure does not need to rely on the knowledge of the true model, because any mistakes made in model fitting would be carried over in explaining the features. The second dimension, \(\mathcal{D}2\), states that an interpretable measure should be able to indicate the impact of a combination of variables on the response variable. This means that any inclusion of influential variables would increase this measure, whereas any injection of noisy and useless variables would decrease this measure. This desirable property allows human users to directly compare the impact of the features when any classifier is trained to make prediction decisions. Though we provided detailed work with an arbitrary image data set, the proposed method can be generalized and adapted to any big data problem. Moreover, it opens up future possibilities for feature selection and dimension reduction in any large-scale and high-dimensional data set. Last, the third dimension, \(\mathcal{D}3\), associates an interpretable measure with the predictivity of a set of features. This property benefits human users because it allows us to establish connections and foresee the potential prediction performance (such as AUC values) that a set of features can deliver before any model fitting procedure. **An ICNN. ** To address the XAI problems heuristically described above, this paper introduced a novel design of an explainable and self-interpretable interaction-based convolutional neural network (ICNN). **We provided a flexible approach to contribute to the major issues regarding explainability, interpretability, transparency, and trustworthiness in black-box algorithms. We introduced and implemented a nonparametric and interaction-based feature selection methodology and used this as a replacement for predefined filters that are widely used in ultra-deep CNNs. Under this paradigm, we presented an ICNN that extracts important features. The proposed architecture uses these extracted features to construct influential and predictive variable modules that are directly associated with the predictivity of the response variable. The proposed design and its many characteristics provide an extremely flexible pipeline that can learn, extract useful information, and identify the hidden potential from any large-scale or high-dimensional data set. ** The proposed methods were presented with both artificial examples and real data applications to COVID-19 chest X-ray image data. We conclude from both simulation and empirical application results that the I-score has unparalleled potential to explain informative and influential local information in large-scale data sets. High I-score values suggest that local information possesses the capability to have higher lower bounds of the predictivity, which thus leads not only to highly accurate prediction performance but also strong explanatory power.