Saeid Tahmasebi

This thesis forms part of wider research that is currently being carried out on complex systems. The main problem related to this concept is how different parts of such a system interact with each other. This issue is addressed by using graphical models, one of the most powerful tools to model data and make statistical inferences. Gaussian graphical models (GGMs) are commonly used for modeling, as they provide tractable inferences in complex models. However, if a dataset contains outliers, GGMs are not effective anymore. To overcome this difficulty, we use t-distributions as they have higher variance leading to fatter tails at both sides of the bell curve than the Gaussian distribution tails. We introduce the fundamental concepts and properties of Gaussian graphical models (GGMs) and Graph Neural Networks (GNNs), setting the stage for the new methods and discussions. We delve into Bayesian structure learning within GGMs, highlighting how Bayesian inference can be used to learn the structure of these models while incorporating prior knowledge. We extend the Bayesian framework to t-distribution graphical models, addressing the complexities of working with heavy-tailed data and improving model robustness. We also provide an overview of the fundamental concepts and properties of Graph Attention Network (GAT), demonstrating how it enhances classification by focusing on the most relevant relationships between nodes in a graph. Finally, we apply the methods from the previous to classify random variables within given graphical models, evaluating their performance through simulations and real-world datasets.