BUGTGNN: Bayesian Uncertainty and Game Theory for Enhancing Graph Neural Networks through Mathematical Analysis

The ongoing COVID-19 pandemic has emphasized the critical need for rapid and accurate diagnostic methods. Precise classification of chest X-ray images into COVID-19 and non-COVID-19 cases serves as a pivotal tool in effective disease management and control. Existing methods often suffer from trade-offs between accuracy, precision, and computational efficiency, hindering their practical utility. Current approaches mainly rely on traditional machine learning algorithms or Convolutional Neural Networks (CNNs), which while effective, still present limitations in terms of sensitivity, specificity, and computational speed. These constraints necessitate the exploration of innovative techniques for improving classification metrics across multiple dimensions. In this work, we introduce a novel framework for optimizing Graph Neural Networks (GNNs) through mathematical analysis, specifically incorporating spectral methods, dynamic graph sparsification, game-theoretic attention mechanisms, Bayesian uncertainty models, and advanced graph partitioning techniques. When applied to the classification of COVID-19 chest X-rays, our model demonstrated significant improvements—increasing precision by 8.3%, accuracy by 8.5%, recall by 4.9%, specificity by 4.5%, and the Area Under the Curve (AUC) by 5.9%, while simultaneously reducing computational delay by 10.5% across multiple datasets. The proposed optimization strategies showcase the power of interdisciplinary approaches in advancing machine learning techniques for medical applications. The demonstrated improvements in classification metrics and computational efficiency highlight the model's potential for broader adoption in healthcare settings, providing a robust, fast, and more accurate tool for COVID-19 diagnosis.