Unfaithful Probability Distributions in Binary Triple of Causality Directed Acyclic Graph
This work addresses a theoretical limitation in causal inference for researchers, though it appears incremental as it builds on known unfaithfulness issues in binary DAGs.
The paper constructs examples of unfaithful probability distributions in three-vertex binary causal DAGs, which violate the faithfulness assumption foundational to causal discovery and inference, and provides a general unfaithful distribution with multiple independence and conditional independence properties.
Faithfulness is the foundation of probability distribution and graph in causal discovery and causal inference. In this paper, several unfaithful probability distribution examples are constructed in three--vertices binary causality directed acyclic graph (DAG) structure, which are not faithful to causal DAGs described in J.M.,Robins,et al. Uniform consistency in causal inference. Biometrika (2003),90(3): 491--515. And the general unfaithful probability distribution with multiple independence and conditional independence in binary triple causal DAG is given.