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

Researchers develop a new causal discovery method for identifying cause-effect relationships in data with hidden variables and non-additive noise, proving identifiability under location-scale noise models and introducing the LSNM-UV algorithm that outperforms existing additive approaches on heteroscedastic data.

This research addresses a fundamental challenge in causal inference: recovering causal structure when some variables are unobserved and noise characteristics vary with the data. Traditional causal discovery methods assume additive noise—where causes only affect the average value of their effects—but real-world phenomena often involve modulation of variance, known as heteroscedasticity. The study proves that acyclic directed mixed graphs meeting a bow-free condition become identifiable under location-scale noise models, marking the first identifiability result for causally insufficient settings beyond additive assumptions. The LSNM-UV algorithm implementing these theoretical advances demonstrates practical improvements over existing baselines on heteroscedastic data, suggesting the framework captures real-world complexity better than prior approaches. The research bridges the gap between theoretical causal inference and practical machine learning applications where variance heterogeneity is common across domains—from financial returns and climate models to biomedical data. For researchers developing causal discovery tools, this work expands the toolkit for scenarios previously thought intractable without additional assumptions or perfect observability. The theoretical guarantees combined with algorithmic completeness provide confidence that the method reliably identifies causal structures rather than producing spurious relationships. This contribution matters to anyone building interpretable machine learning systems or conducting causal analysis on high-dimensional observational data where hidden confounders and non-constant variance are realistic concerns. The work likely influences subsequent developments in causal machine learning, pushing the field toward methods handling increasingly realistic data-generating processes.

• →First identifiability result for hidden-variable causal models under non-additive location-scale noise, extending beyond traditional additive noise assumptions
• →LSNM-UV algorithm proves sound and complete with demonstrated performance gains on heteroscedastic data compared to additive baselines
• →Bow-free condition on acyclic directed mixed graphs enables causal direction identification even when primary assumptions are violated
• →Research addresses practical gap where causes modulate both mean and variance of effects, common in real-world systems
• →Theoretical advances enable reliable causal structure recovery from observational data despite hidden confounders