State-Of-The-Art and Challenges in Causal Inference on Graphs: Confounders and Interferences

Causal inference on graphs has emerged as a critical area of research, with applications ranging from epidemiology to social networks and economics. In graph-structured data, estimating causal effects poses significant challenges, primarily due to the presence of confounding (including non-local confounding) and interference (violations of the Stable Unit Treatment Value Assumption, SUTVA), where the treatment of one node can influence the outcomes of other nodes. This work provides a comprehensive overview of methods developed to address these challenges, focusing on static and dynamic graphs. We categorize methods based on their ability to handle observed and unobserved confounding, interference, or both. We also explore the practical applications of these methods in various domains, demonstrating how they are used to address real-world causal inference problems. Finally, we identify key challenges in this field and suggest future directions for addressing them.