mlsanityData to 7 Oct 2026

On the Identifiability of Causal Graphs with the Invariance Principle

arXiv 2510.13583 ↗First posted 15 Oct 2025stat.ML cs.LGcited by 0

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Abstract (arXiv)

Causal discovery from i.i.d. observational data is known to be generally ill-posed. We demonstrate that if we have access to the distribution induced by a structural causal model, and additional data from (in the best case) textitonly two environments that sufficiently differ in the noise statistics, the unique causal graph is identifiable. Notably, this is the first result in the literature that guarantees the entire causal graph recovery with a constant number of environments and arbitrary nonlinear mechanisms. Our only constraint is the Gaussianity of the noise terms; however, we propose potential ways to relax this requirement. Of interest on its own, we expand on the well-known duality between independent component analysis (ICA) and causal discovery; recent advancements have shown that nonlinear ICA can be solved from multiple environments, at least as many as the number of sources: we show that the same can be achieved for causal discovery while having access to much less auxiliary information.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 34 of its 57 references that are in the map. First posted on arXiv 15 Oct 2025.

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References · 34

  1. 2015Causal inference using invariant prediction: identification and confidence intervalscited by 533
  2. 2019Variational Autoencoders and Nonlinear ICA: A Unifying Frameworkcited by 494
  3. 2018Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learningcited by 278
  4. 2016Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICAcited by 270
  5. 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
  6. 2020Differentiable Causal Discovery from Interventional Datacited by 218
  7. 2019Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changescited by 166
  8. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  9. 2021Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICAcited by 158
  10. 2017Invariant Causal Prediction for Nonlinear Modelscited by 140
  11. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  12. 2020ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICAcited by 102
22 more
  1. 2019The Incomplete Rosetta Stone Problem: Identifiability Results for Multi-View Nonlinear ICAcited by 86
  2. 2018Characterizing and Learning Equivalence Classes of Causal DAGs under Interventionscited by 76
  3. 2020Hidden Markov Nonlinear ICA: Unsupervised Learning from Nonstationary Time Seriescited by 76
  4. 2021Disentangling Identifiable Features from Noisy Data with Structured Nonlinear ICAcited by 64
  5. 2017Gradient Estimators for Implicit Modelscited by 58
  6. 2019Causal Discovery with General Non-Linear Relationships Using Non-Linear ICAcited by 58
  7. 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
  8. 2022Causal Discovery in Heterogeneous Environments Under the Sparse Mechanism Shift Hypothesiscited by 54
  9. 2022Function Classes for Identifiable Nonlinear Independent Component Analysiscited by 53
  10. 2017Inference via low-dimensional couplingscited by 43
  11. 2023Scalable Causal Discovery with Score Matchingcited by 42
  12. 2023Causal Discovery with Score Matching on Additive Models with Arbitrary Noisecited by 41
  13. 2022Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Modelcited by 38
  14. 2015backShift: Learning causal cyclic graphs from unknown shift interventionscited by 37
  15. 2022Learning Causal Representations of Single Cells via Sparse Mechanism Shift Modelingcited by 33
  16. 2017Learning Causal Structures Using Regression Invariancecited by 32
  17. 2024Score-based Causal Representation Learning: Linear and General Transformationscited by 27
  18. 2024Demystifying amortized causal discovery with transformerscited by 10
  19. 2024Score matching through the roof: linear, nonlinear, and latent variables causal discoverycited by 8
  20. 2025Distinguishing Cause from Effect with Causal Velocity Modelscited by 6
  21. 2025Multi-Domain Causal Discovery in Bijective Causal Modelscited by 4
  22. 2019Likelihood-Free Overcomplete ICA and Applications in Causal Discoverycited by 2

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