Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variables

2026-06-06

AI Summary

This study addresses the identifiability of causal structures in the presence of latent variables under location-scale noise models, which generalize beyond additive noise assumptions. The authors establish, for the first time, that acyclic directed mixed graphs (ADMGs) satisfying the bow-free condition are identifiable under such models, and further provide sufficient conditions for identifiability of causal directions even when the bow-free condition is violated. Building on this theoretical foundation, they propose a two-stage algorithm, LSNM-UV. Experimental results demonstrate that the proposed method significantly outperforms existing approaches based on additive noise models on heteroscedastic data, thereby validating both the correctness and practical advantage of the developed theory.

Abstract

We study causal discovery from observational data when some variables are hidden and the data-generating process follows a location-scale noise model (LSNM). Existing methods that handle hidden confounders typically assume additive noise, but in practice, causes often modulate not just the mean but also the variance of their effects. We prove that acyclic directed mixed graphs (ADMGs) satisfying a bow-free condition are identifiable under LSNM with hidden variables, establishing the first identifiability result for causally insufficient models beyond noise additivity. We further provide sufficient conditions for identifying causal direction even when the bow-free assumption is violated. Our two-stage algorithm, LSNM-UV, is sound and complete, and experiments demonstrate improved performance over additive baselines on heteroscedastic data.

Problem

• causal discovery
• hidden variables
• location-scale noise model
• non-additive noise
• identifiability

Innovation

• location-scale noise model
• causal discovery
• hidden variables
• identifiability
• bow-free ADMG