Score-based Greedy Search for Structure Identification of Partially Observed Linear Causal Models

2025-10-05

AI Summary

This paper addresses the structural identifiability problem for partially observable linear causal systems with latent variables. We propose the first score-based greedy search method with theoretical identifiability guarantees. Our approach introduces: (1) a generalized *N*-factor model and a global consistency theory, ensuring unique identifiability of latent-variable causal graphs; (2) the Latent-variable Greedy Equivalence Search (LGES) algorithm, which exactly recovers the true causal structure within its Markov equivalence class; and (3) a constrained equivalence-class search mechanism coupled with explicit latent-graph operators to enhance both computational efficiency and robustness. Experiments on synthetic and real-world datasets demonstrate that LGES significantly outperforms existing methods in accurately recovering latent-variable causal graphs, while providing rigorous theoretical guarantees on identifiability and consistency.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Search and Optimization: Learning to Search

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• 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

Identifying the structure of a partially observed causal system is essential to various scientific fields. Recent advances have focused on constraint-based causal discovery to solve this problem, and yet in practice these methods often face challenges related to multiple testing and error propagation. These issues could be mitigated by a score-based method and thus it has raised great attention whether there exists a score-based greedy search method that can handle the partially observed scenario. In this work, we propose the first score-based greedy search method for the identification of structure involving latent variables with identifiability guarantees. Specifically, we propose Generalized N Factor Model and establish the global consistency: the true structure including latent variables can be identified up to the Markov equivalence class by using score. We then design Latent variable Greedy Equivalence Search (LGES), a greedy search algorithm for this class of model with well-defined operators, which search very efficiently over the graph space to find the optimal structure. Our experiments on both synthetic and real-life data validate the effectiveness of our method (code will be publicly available).

Problem

• Identifying causal structure with latent variables using score-based methods
• Developing greedy search algorithm for partially observed linear models
• Ensuring identifiability guarantees for latent variable causal discovery

Innovation

• Score-based greedy search for latent variables
• Generalized N Factor Model with identifiability guarantees
• Latent variable Greedy Equivalence Search algorithm