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

2026-06-06 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, quick

Summary

A new study addresses causal discovery from observational data in location-scale noise models (LSNM) that include hidden variables. Traditional methods for handling hidden confounders typically assume additive noise, which limits their applicability when causes influence both the mean and variance of their effects, a common scenario known as heteroscedasticity. This research establishes the first identifiability result for causally insufficient models beyond noise additivity, proving that acyclic directed mixed graphs (ADMGs) satisfying a bow-free condition are identifiable under LSNM with hidden variables. Furthermore, the study provides sufficient conditions for identifying causal direction even when the bow-free assumption is violated. The authors introduce a two-stage algorithm, LSNM-UV, which is demonstrated to be sound and complete. Experimental results show improved performance over additive baselines when applied to heteroscedastic data. The paper was published on 2026-06-06.

Key takeaway

For research scientists working on causal inference with observational data, especially when hidden variables and heteroscedasticity are present, you should consider the LSNM-UV algorithm. This method extends causal discovery beyond traditional additive noise assumptions, allowing you to identify causal directions even when causes modulate both the mean and variance of effects. Incorporating LSNM-UV can improve the accuracy of your causal models on real-world, complex datasets.

Key insights

Causal discovery in location-scale noise models with hidden variables is identifiable, even when causes affect both mean and variance.

Principles

• Bow-free ADMGs are identifiable under LSNM with hidden variables.
• Causal direction can be identified even if bow-free assumption is violated.

Method

LSNM-UV is a two-stage algorithm for causal discovery in LSNM with hidden variables, demonstrated to be sound and complete.

In practice

• Apply LSNM-UV for causal discovery in heteroscedastic data.
• Consider LSNM when causes modulate effect variance.

Topics

• Causal Discovery
• Location-Scale Noise Models
• Hidden Variables
• Heteroscedasticity
• ADMGs
• LSNM-UV Algorithm

Best for: AI Scientist, Research Scientist, Machine Learning Engineer

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.