计数数据的因果有向无环图识别：基于泊松稀疏结构方程模型
Causal DAG Identification for Count Data via Poisson Thinning Structural Equation Models
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中文总结 AI 辅助
针对计数数据因果DAG识别问题，提出泊松稀疏结构方程模型（PT-SEM），在正则条件下实现DAG、系数及外生分布的可识别性，并开发基于动态规划BIC的结构学习算法，模拟与真实数据验证其有效性。
中文摘要 AI 辅助
计数型变量出现在许多科学和应用场景中，然而，允许从观测数据中完全识别因果有向无环图（DAG）的显式结构模型仍然有限。泊松分支结构因果模型（PB-SCM）通过使用二项稀疏和独立的泊松外生变量，提供了线性结构方程模型的计数型模拟，但其因果DAG通常仅能部分识别。在此框架基础上，我们提出了泊松稀疏结构方程模型（PT-SEM），该模型将PB-SCM中的二项稀疏替换为泊松稀疏，并允许节点级外生分布来自多种计数分布族。在节点级正则性条件下，我们建立了因果DAG、稀疏系数及节点级外生分布的可识别性。相同的识别分析也扩展到二项稀疏，每当所有非汇节点具有非泊松外生噪声时，即可实现完全可识别性。我们进一步开发了一种结构学习算法，该算法通过动态规划优化基于局部似然（在插件矩估计处评估）的BIC分数，并证明了其在DAG选择上的一致性。模拟实验展示了在DAG恢复和稀疏系数估计方面的优越性能，真实数据应用则说明了PT-SEM的实际效用。
英文摘要
Count-valued variables arise in many scientific and applied settings, yet explicit structural models that allow full identification of causal DAGs from observational data remain limited. The Poisson branching structural causal model (PB-SCM) provides a count-valued analogue of linear structural equation models using binomial thinning and independent Poisson exogenous variables, but its causal DAG is generally only partially identifiable. Building on this framework, we propose the Poisson thinning structural equation model (PT-SEM), which replaces binomial thinning in PB-SCM with Poisson thinning and allows node-wise exogenous distributions from diverse count-distribution families. Under node-wise regularity conditions, we establish identifiability of the causal DAG, the thinning coefficients, and the node-wise exogenous distributions. The same identification analysis extends to binomial thinning, yielding full identifiability whenever every nonsink has non-Poisson exogenous noise. We further develop a structure learning algorithm that optimizes, via dynamic programming, a BIC score based on local likelihoods evaluated at plug-in moment estimates, and establish its consistency for DAG selection. Simulations demonstrate favorable performance in DAG recovery and thinning-coefficient estimation, and a real-data application illustrates the practical utility of PT-SEM.
发表机构
- Graduate School of Informatics（信息学研究生院）
- Kyoto University（京都大学）
- Institute for Liberal Arts and Sciences（文理学院）
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