Causal Additive Models with Unobserved Causal Paths and Backdoor Paths

TL;DR

This paper develops new theoretical conditions and an algorithm for identifying causal directions in additive models even when hidden variables and unobserved paths exist, advancing causal discovery methods.

Contribution

It introduces novel conditions for causal identification in models with unobserved paths and provides a complete algorithm with empirical validation.

Findings

Conditions enable identification of parent-child relationships in complex cases

Algorithm achieves competitive performance on benchmark datasets

New characterizations of regression sets improve causal inference

Abstract

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.