Identification of Causal Direction under an Arbitrary Number of Latent Confounders

2025-10-26

AI Summary

This paper addresses the problem of identifying the causal direction between two observed variables in the presence of an arbitrary number of latent confounders. Existing methods rely on strong, unverifiable structural assumptions about latent variables—such as single-latent-variable models or absence of interaction effects—which severely limit practical applicability. To overcome this, we propose a novel method grounded in the rank-deficiency properties of higher-order cumulant matrices: under a linear non-Gaussian framework, we construct the joint higher-order cumulant matrix of the observed variables, whose rank deficiency direction directly determines the causal direction. Our approach imposes no constraints on the number or structure of latent confounders and avoids iterative optimization. We provide theoretical guarantees for causal identifiability and asymptotic consistency. Extensive experiments demonstrate its robustness and superior performance in complex confounding scenarios.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

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
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Recovering causal structure in the presence of latent variables is an important but challenging task. While many methods have been proposed to handle it, most of them require strict and/or untestable assumptions on the causal structure. In real-world scenarios, observed variables may be affected by multiple latent variables simultaneously, which, generally speaking, cannot be handled by these methods. In this paper, we consider the linear, non-Gaussian case, and make use of the joint higher-order cumulant matrix of the observed variables constructed in a specific way. We show that, surprisingly, causal asymmetry between two observed variables can be directly seen from the rank deficiency properties of such higher-order cumulant matrices, even in the presence of an arbitrary number of latent confounders. Identifiability results are established, and the corresponding identification methods do not even involve iterative procedures. Experimental results demonstrate the effectiveness and asymptotic correctness of our proposed method.

Problem

• Identifies causal direction under latent confounders
• Uses higher-order cumulants for causal asymmetry detection
• Handles arbitrary latent variables without iterative procedures

Innovation

• Uses higher-order cumulant matrices for causal identification
• Detects causal asymmetry through rank deficiency analysis
• Handles arbitrary latent confounders without iterative procedures