揭示三节点因果图中概率分布不忠实的构造方法
Unfaithful Probability Distributions in Binary Triple of Causality Directed Acyclic Graph
- 构建三顶点二值因果有向无环图中的不忠实概率分布实例
- 给出多独立与条件独立共存的通用不忠实分布形式
- 为因果推断中的忠实性假设提供反例支持
忠实性是因果发现与因果推断中概率分布与图结构的基础。本文在三顶点二值因果有向无环图（DAG）结构中，构造了多个不忠实于J.M. Robins等（Biometrika, 2003）所描述因果DAG的概率分布实例。同时，给出了具有多重独立性和条件独立性的二值三元因果DAG的通用不忠实概率分布形式。这些结果揭示了忠实性假设在实际应用中的局限性，为因果推断的理论边界提供了重要参考。
原文摘要 · Abstract (English)
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.
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