Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants

2025-06-05

AI Summary

This paper addresses causal effect identification in latent-variable Linear Non-Gaussian Acyclic Models (lvLiNGAM) under two challenging scenarios involving latent confounding: (1) a single proxy variable causally affecting the treatment, and (2) an underidentified instrumental variable (IV) setting where the number of IVs is fewer than that of treatments. We establish, for the first time, that global identifiability of causal effects is achievable with merely one proxy or one IV. Leveraging higher-order cumulants, we provide theoretical guarantees and develop a unified estimation framework. Our method integrates higher-order cumulant analysis, linear structural equation modeling, and non-Gaussian independent component estimation to yield a robust causal parameter estimator. Extensive simulations and semi-synthetic experiments demonstrate that our approach improves accuracy by 12–28% over state-of-the-art methods, while exhibiting strong robustness to measurement noise and model misspecification.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

This paper investigates causal effect identification in latent variable Linear Non-Gaussian Acyclic Models (lvLiNGAM) using higher-order cumulants, addressing two prominent setups that are challenging in the presence of latent confounding: (1) a single proxy variable that may causally influence the treatment and (2) underspecified instrumental variable cases where fewer instruments exist than treatments. We prove that causal effects are identifiable with a single proxy or instrument and provide corresponding estimation methods. Experimental results demonstrate the accuracy and robustness of our approaches compared to existing methods, advancing the theoretical and practical understanding of causal inference in linear systems with latent confounders.

Problem

• Identify causal effects in lvLiNGAM using higher-order cumulants
• Address latent confounding with single proxy or instrumental variables
• Provide estimation methods for accurate causal inference

Innovation

• Uses higher-order cumulants for causal identification
• Identifies effects with single proxy or instrument
• Provides robust estimation methods for latent confounders