Causal Additive Models with Unobserved Causal Paths and Backdoor Paths
This work addresses a long-standing problem in causal discovery, particularly for researchers and practitioners dealing with complex causal relationships in the presence of hidden variables.
The authors tackled the problem of causal discovery in the presence of unobserved causal paths and backdoor paths, and established sufficient conditions for identifying causal directions in many such cases, with competitive performance to state-of-the-art methods. Their approach enables identification of the parent-child relationship in a bow, a notoriously difficult case in causal discovery.
Causal additive models provide a tractable yet expressive framework for causal discovery in the presence of hidden variables. However, when unobserved backdoor or causal paths exist between two variables, their causal relationship is often unidentifiable under existing theories. We establish sufficient conditions under which causal directions can be identified in many such cases. In particular, we derive conditions that enable identification of the parent-child relationship in a bow, an adjacent pair of observed variables sharing a hidden common parent. This represents a notoriously difficult case in causal discovery, and, to our knowledge, no prior work has established such identifiability in any causal model without imposing assumptions on the hidden variables. Our conditions rely on new characterizations of regression sets and a hybrid approach that combines independence among regression residuals with conditional independencies among observed variables. We further provide a sound and complete algorithm that incorporates these insights, and empirical evaluations demonstrate competitive performance with state-of-the-art methods.