Local Identifying Causal Relations in the Presence of Latent Variables

We tackle the problem of identifying whether a variable is the cause of a specified target using observational data. State-of-the-art causal learning algorithms that handle latent variables typically rely on identifying the global causal structure, often represented as a partial ancestral graph (PAG), to infer causal relationships. Although effective, these approaches are often redundant and computationally expensive when the focus is limited to a specific causal relationship. In this work, we introduce novel local characterizations that are necessary and sufficient for various types of causal relationships between two variables, enabling us to bypass the need for global structure learning. Leveraging these local insights, we develop efficient and fully localized algorithms that accurately identify causal relationships from observational data. We theoretically demonstrate the soundness and completeness of our approach. Extensive experiments on benchmark networks and two real-world datasets further validate the effectiveness and efficiency of our method.