Identifiability of latent causal graphical models without pure children

2025-05-23

AI Summary

Causal discovery in latent-variable graphical models faces fundamental identifiability limitations under realistic constraints—such as the absence of pure children and single-modality observed variables. Method: This paper introduces the “double-triangle graph” structural condition, enabling global identifiability of the entire causal graph under nonparametric measurement models. Contribution/Results: For the first time, it establishes rigorous identifiability theory for latent causal graphs without assuming pure children, deriving necessary conditions and characterizing fundamental identifiability limits. Compared to classical approaches—e.g., requiring multiple pure children or imposing strong restrictions on the latent graph—the double-triangle condition significantly weakens prior assumptions. We prove its sufficiency for global identifiability and validate via simulations that it enables high-precision recovery of latent structures. This work provides a novel paradigm for causal discovery in complex latent-variable systems.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Graphical Models
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

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.

Problem

• Identifying causal models with latent variables
• Relaxing strict identifiability conditions for latent graphs
• Handling mixed observed variable types and binary latents

Innovation

• Nonparametric measurement model with arbitrary observed variables
• Double triangular graphical condition for identifiability
• Relaxes pure children condition for latent variables