提出新条件，让有隐变量的因果模型更易识别。
On Theoretical Identifiability of Discrete Latent Causal Graphical Models
- 用双重三角结构代替传统纯子节点限制，放宽识别条件。
- 在任意观测变量类型和二值隐变量下，保证整个因果图可识别。
- 适用于复杂现实数据，对隐变量分析有理论指导意义。
本文研究存在隐变量时因果图模型的可识别性问题。现有条件常要求每个隐变量有多个纯子节点或对隐因果图施加限制，且所有观测变量同质，导致实际应用受限。本文考虑任意观测变量类型与二值隐变量的非参数测量模型，提出双重三角图形条件，可保证整个因果图的可识别性，显著弱化了常见的纯子节点条件。同时建立了可识别性的必要条件，揭示了识别能力的根本极限。模拟实验表明，满足该条件的隐结构能从数据中准确估计。
原文摘要 · Abstract (English)
This paper considers a challenging problem of identifying a causal graphical model under the presence of latent variables. While various identifiability conditions have been proposed in the literature, they often require multiple pure children per latent variable or restrictions on the latent causal graph. Furthermore, it is common for all observed variables to exhibit the same modality. Consequently, the existing identifiability conditions are often too stringent for complex real-world data. We consider a general nonparametric measurement model with arbitrary observed variable types and binary latent variables, and propose a double triangular graphical condition that guarantees identifiability of the entire causal graphical model. The proposed condition significantly relaxes the popular pure children condition. We also establish necessary conditions for identifiability and provide valuable insights into fundamental limits of identifiability. Simulation studies verify that latent structures satisfying our conditions can be accurately estimated from data.
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