Unfaithful Probability Distributions in Binary Triple of Causality Directed Acyclic Graph

2025-01-30

AI Summary

This paper addresses the fragility of the faithfulness assumption in causal discovery, focusing on the minimal nontrivial causal structure—binary three-node directed acyclic graphs (DAGs). Method: Integrating causal graph theory, discrete probabilistic modeling, and algebraic construction techniques for binary variables, we systematically construct and explicitly characterize multiple classes of unfaithful probability distributions. We propose, for the first time, a general framework for generating unfaithful distributions that satisfy arbitrary combinations of marginal and conditional independence constraints. Contribution/Results: We rigorously prove that faithfulness does not hold universally for this fundamental model, precisely delineating its failure boundary. Our work provides the first analytically tractable, fully reproducible toolkit of unfaithful counterexamples. These results establish a critical theoretical benchmark for assessing robustness in causal inference, modeling unfaithful scenarios, and designing faithfulness tests.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Causal Inference
• Graphical Models
• Anomalous Behavior

Innovation

• Causal Graphs
• Probability Distributions
• Faithfulness Assumption