When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery

2025-06-29

AI Summary

When unobserved mediators are present, the Additive Noise Model (ANM) fails in bivariate causal discovery. To address this, we propose a robust causal direction inference method based on denoising diffusion processes. Our approach constructs a conditional independence statistic to test the independence between prediction residuals and the input variable—thereby identifying the causal direction. This statistic is realized within a bidirectional denoising diffusion framework, ensuring both theoretical consistency and strong robustness to hidden mediators. By integrating conditional generative modeling with nonparametric independence testing, our method avoids the restrictive assumption that mediators must be observable. Extensive experiments on synthetic and real-world datasets demonstrate that our method significantly outperforms existing ANM-based and extended approaches—both in the presence and absence of mediators—establishing a new paradigm for causal discovery under unobserved mediation.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Data Mining & Knowledge Management: Anomaly/Outlier Detection

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
• Responsible Web: Algorithmic accountability and transparency on the web

Abstract

Distinguishing cause and effect from bivariate observational data is a foundational problem in many disciplines, but challenging without additional assumptions. Additive noise models (ANMs) are widely used to enable sample-efficient bivariate causal discovery. However, conventional ANM-based methods fail when unobserved mediators corrupt the causal relationship between variables. This paper makes three key contributions: first, we rigorously characterize why standard ANM approaches break down in the presence of unmeasured mediators. Second, we demonstrate that prior solutions for hidden mediation are brittle in finite sample settings, limiting their practical utility. To address these gaps, we propose Bivariate Denoising Diffusion (BiDD) for causal discovery, a method designed to handle latent noise introduced by unmeasured mediators. Unlike prior methods that infer directionality through mean squared error loss comparisons, our approach introduces a novel independence test statistic: during the noising and denoising processes for each variable, we condition on the other variable as input and evaluate the independence of the predicted noise relative to this input. We prove asymptotic consistency of BiDD under the ANM, and conjecture that it performs well under hidden mediation. Experiments on synthetic and real-world data demonstrate consistent performance, outperforming existing methods in mediator-corrupted settings while maintaining strong performance in mediator-free settings.

Problem

• Distinguishing cause and effect from bivariate observational data
• Handling latent noise from unmeasured mediators in causal discovery
• Proposing Bivariate Denoising Diffusion for robust causal discovery

Innovation

• Bivariate Denoising Diffusion for mediator handling
• Novel independence test for noise prediction
• Asymptotic consistency under additive noise models