发表机构
Department of Information and Computing Sciences, Utrecht University; Leiden Institute of Advanced Computer Science, Leiden University（乌得勒支大学信息与计算科学系; 莱顿大学莱顿高级计算机科学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究贝叶斯因果发现在潜在混杂下的行为，聚焦线性高斯因果模型中两观测变量的加性潜在混杂。推导关键相关阈值，刻画两种后验失败模式，通过精确后验计算验证，揭示其在潜在混杂下的结构后果。
AI 中文摘要
贝叶斯因果发现因其能通过后验推断量化有向无环图（DAG）上的认知不确定性而被广泛使用。然而，其在潜在混杂下的行为仍知之甚少，因为现有工作通常指出混杂会破坏可识别性，但未刻画DAG的后验分布如何响应。在这项工作中，我们分析线性高斯因果模型中潜在混杂下的后验行为，聚焦于恰好两个观测变量之间的加性潜在混杂。我们推导了一个关键相关阈值，高于此阈值，得分函数倾向于在混杂变量之间有虚假边的图，并表明该阈值随样本量减小——更多数据降低了虚假边被青睐所需的相关性。超过此阈值，我们刻画了由混杂变量周围局部结构决定的两种不同的后验失败模式。我们的发现得到了对多个图结构的精确后验计算的支持，展示了预测的失败模式。
英文摘要
Bayesian causal discovery is widely used for its ability to quantify epistemic uncertainty over directed acyclic graphs (DAGs) through posterior inference. However, its behaviour under latent confounding remains poorly understood, as existing work typically notes that confounding breaks identifiability without characterising how the posterior distribution over DAGs responds. In this work, we analyse posterior behaviour under latent confounding in linear Gaussian causal models, focusing on additive latent confounding between exactly two observed variables. We derive a critical correlation threshold above which the score function favours graphs with a spurious edge between the confounded variables, and show that this threshold decreases with sample size -- more data lowers the correlation required for the spurious edge to be favoured. Beyond this threshold, we characterize two distinct posterior failure regimes determined by the local structure around the confounded variables. Our findings are supported by exact posterior computations on multiple graph structures, demonstrating both the predicted failure regimes.
