Latent Variable Causal Discovery under Selection Bias

2025-12-11

AI Summary

This paper addresses the identifiability of latent-variable causal structures under selection bias. Recognizing the failure of conventional conditional independence–based methods in biased settings, we first extend covariance submatrix rank constraints to selection-biased scenarios and develop a unified graphical framework integrating causal graphs with selection mechanisms. Theoretically, we prove that rank information simultaneously encodes both the latent causal structure and the selection mechanism; under linear Gaussian assumptions, this enables unique identification of classical single-factor models. Simulation studies and real-data experiments demonstrate that our method substantially improves accuracy in latent causal discovery under selection bias. By leveraging rank-based structural constraints, the approach provides a novel, bias-robust paradigm for causal discovery—moving beyond reliance on conditional independence and offering theoretical guarantees where traditional methods break down.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Addressing selection bias in latent variable causal discovery is important yet underexplored, largely due to a lack of suitable statistical tools: While various tools beyond basic conditional independencies have been developed to handle latent variables, none have been adapted for selection bias. We make an attempt by studying rank constraints, which, as a generalization to conditional independence constraints, exploits the ranks of covariance submatrices in linear Gaussian models. We show that although selection can significantly complicate the joint distribution, interestingly, the ranks in the biased covariance matrices still preserve meaningful information about both causal structures and selection mechanisms. We provide a graph-theoretic characterization of such rank constraints. Using this tool, we demonstrate that the one-factor model, a classical latent variable model, can be identified under selection bias. Simulations and real-world experiments confirm the effectiveness of using our rank constraints.

Problem

• Addresses selection bias in latent variable causal discovery
• Uses rank constraints to identify causal structures under bias
• Demonstrates identification of one-factor model with selection bias

Innovation

• Rank constraints generalize conditional independencies for latent variables
• Rank constraints preserve causal structure under selection bias
• Graph-theoretic characterization enables identification of one-factor models