Learning and Characterization of Interventional Equivalence class of Causal Graphs with Latents

Abstract: Directed Causal Graphs (DAGs) capture causal relationships amongst a set of variables and they specify how interventional distributions relate to observational ones. Unobserved latent variables  are represented in DAGs with edges having double arrows. Celebrated``do-calculus” introduced by Pearl relates invariances in interventional distributions to a specific causal graph with latents embodying expert knowledge. We consider the reverse problem of learning the equivalence class of causal graphs that could imply the observed invariances of the do-calculus. Given observational and interventional data obtained under soft interventions with known targets, we provide a complete characterization of the equivalence class of Causal DAGs. We also provide a sound learning algorithm to learn the equivalence class under additional faithfulness assumptions.