Causal Discovery over Clusters of Variables in Markovian Systems
Tara Anand, Adèle Ribeiro, Jin Tian, George Hripcsak, Elias Bareinboim
Causal discovery approaches are limited by scalability and interpretability, and are primarily for learning relationships among variables. Learning causal relationships among sets or clusters of variables is of interest as for some applications, relationships among variables grouped in semantically meaningful ways is the goal, and in others, clusters improve causal discovery in high-dimensions by reducing dimensionality. Here, we introduce an approach for learning over clusters in Markov causal systems. We develop a new graphical model to encode knowledge of relationships between user-defined clusters while fully representing independencies and dependencies over clusters, faithful to a specific distribution. Then we define and characterize a graphical equivalence class of these models that share cluster-level independence information. Lastly, we introduce an algorithm for causal discovery, leveraging these new representations, to soundly represent learnable causal relationships between clusters of variables.