Unfaithful Probability Distributions in Binary Triple of Causality Directed Acyclic Graph

TL;DR

This paper constructs examples of unfaithful probability distributions in binary triple causality DAGs, challenging the assumption that distributions are always faithful to the causal structure, and extends to general cases with multiple independencies.

Contribution

It introduces specific unfaithful distributions in binary triple DAGs and generalizes to cases with multiple independencies, highlighting limitations of faithfulness assumption.

Findings

Examples of unfaithful distributions in binary triple DAGs.

General unfaithful distributions with multiple independencies.

Challenges to the faithfulness assumption in causal inference.

Abstract

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.