提出新算法解决重尾分布下因果图的准确发现问题。
A PC Algorithm for Max-Linear Bayesian Networks
- 基于*分离条件改进PC算法，保持一致性。
- 新算法PCstar可定向传统方法无法确定的边。
- 适合研究重尾数据因果推断的学者使用。
最大线性贝叶斯网络（MLBNs）是一类近期提出的结构方程模型，适用于具有重尾分布的随机变量。与大多数有向图模型不同，MLBNs通常不满足d-分离的忠实性，因此经典因果发现算法如PC算法或贪婪等价搜索无法准确恢复真实图结构。本文首次研究了在给定真实未知图中条件独立性查询预言机的情况下，针对MLBNs的约束基础发现算法。我们证明：若预言机由真实图中的*分离准则给出，则即使*分离带来额外的条件独立关系，PC算法仍保持一致性。此外，我们提出一种新算法PCstar，该算法假设对C^*分离的忠实性，能够定向仅用d-或*分离无法定向的边。
原文摘要 · Abstract (English)
Max-linear Bayesian networks (MLBNs) are a relatively recent class of structural equation models which arise when the random variables involved have heavy-tailed distributions. Unlike most directed graphical models, MLBNs are typically not faithful to d-separation and thus classical causal discovery algorithms such as the PC algorithm or greedy equivalence search can not be used to accurately recover the true graph structure. In this paper, we begin the study of constraint-based discovery algorithms for MLBNs given an oracle for testing conditional independence in the true, unknown graph. We show that if the oracle is given by the $\ast$-separation criteria in the true graph, then the PC algorithm remains consistent despite the presence of additional CI statements implied by $\ast$-separation. We also introduce a new causal discovery algorithm named "PCstar" which assumes faithfulness to $C^\ast$-separation and is able to orient additional edges which cannot be oriented with only d- or $\ast$-separation.
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