Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variables
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 13 Oct 2026). Builds on 9 of its 19 references that are in the map. First posted on arXiv 6 Jun 2026.
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9 of 19 references.
References · 9
- 2013Causal Discovery with Continuous Additive Noise Modelscited by 253
- 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 177
- 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
- 2020Causal Discovery with Unobserved Confounding and non-Gaussian Datacited by 24
- 2023Causal Reasoning in the Presence of Latent Confounders via Neural ADMG Learningcited by 15
- 2023Effective Causal Discovery under Identifiable Heteroscedastic Noise Modelcited by 8
- 2023Cause-Effect Inference in Location-Scale Noise Models: Maximum Likelihood vs. Independence Testingcited by 7
- 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
- 2025Causal Additive Models with Unobserved Causal Paths and Backdoor Pathscited by 5
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Citing papers per year: 2026: 1.
1 paper.
- 2026Causal Discovery via Transformed Low-Rank Quantile Surfaces15 Sep 2026