mlsanityData to 7 Oct 2026

On the Identifiability and Estimation of Causal Location-Scale Noise Models

arXiv 2210.09054 ↗First posted 13 Oct 2022stat.ML cs.AI cs.LGcited by 56

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Abstract (arXiv)

We study the class of location-scale or heteroscedastic noise models (LSNMs), in which the effect Y can be written as a function of the cause X and a noise source N independent of X, which may be scaled by a positive function g over the cause, i.e., Y = f(X) + g(X)N. Despite the generality of the model class, we show the causal direction is identifiable up to some pathological cases. To empirically validate these theoretical findings, we propose two estimators for LSNMs: an estimator based on (non-linear) feature maps, and one based on neural networks. Both model the conditional distribution of Y given X as a Gaussian parameterized by its natural parameters. When the feature maps are correctly specified, we prove that our estimator is jointly concave, and a consistent estimator for the cause-effect identification task. Although the the neural network does not inherit those guarantees, it can fit functions of arbitrary complexity, and reaches state-of-the-art performance across benchmarks.

Key facts. Cited by 56 papers in the map (data through 7 Oct 2026). Builds on 17 of its 60 references that are in the map. First posted on arXiv 13 Oct 2022.

Builds on

17 of 60 references.

References · 17

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  3. 2014New insights and perspectives on the natural gradient methodcited by 435
  4. 2013Causal Discovery with Continuous Additive Noise Modelscited by 252
  5. 2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
  6. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  7. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  8. 2021DiBS: Differentiable Bayesian Structure Learningcited by 105
  9. 2020Causal Autoregressive Flowscited by 97
  10. 2016Kernel-based Tests for Joint Independencecited by 40
  11. 2022Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Modelcited by 38
  12. 2016Entropic Causal Inferencecited by 27
5 more
  1. 2018Causal Inference via Kernel Deviance Measurescited by 22
  2. 2017Telling Cause from Effect using MDL-based Local and Global Regressioncited by 21
  3. 2016Conditional distribution variability measures for causality detectioncited by 15
  4. 2018Causal Inference and Mechanism Clustering of A Mixture of Additive Noise Modelscited by 9
  5. 2013Consistency of Causal Inference under the Additive Noise Modelcited by 8

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 17; 2024: 8; 2025: 16; 2026: 15.

56 papers.

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  1. 2023Nonparametric Identifiability of Causal Representations from Unknown Interventionscited by 105
  2. 2023Identifiability of latent-variable and structural-equation models: from linear to nonlinearcited by 58
  3. 2023Counterfactual Identifiability of Bijective Causal Modelscited by 42
  4. 2023Causal Modeling with Stationary Diffusionscited by 19
  5. 2023Partial Counterfactual Identification of Continuous Outcomes with a Curvature Sensitivity Modelcited by 14
  6. 2023Finding Counterfactually Optimal Action Sequences in Continuous State Spacescited by 12
  7. 2024Identifiable Causal Representation Learning: Unsupervised, Multi-View, and Multi-Environmentcited by 12
  8. 2023Bivariate Causal Discovery using Bayesian Model Selectioncited by 11
  9. 2024Demystifying amortized causal discovery with transformerscited by 10
  10. 2023Effective Causal Discovery under Identifiable Heteroscedastic Noise Modelcited by 8
  11. 2023Cause-Effect Inference in Location-Scale Noise Models: Maximum Likelihood vs. Independence Testingcited by 7
  12. 2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7
38 more
  1. 2023Heteroscedastic Causal Structure Learningcited by 6
  2. 2023Scalable Counterfactual Distribution Estimation in Multivariate Causal Modelscited by 6
  3. 2023Robust Estimation of Causal Heteroscedastic Noise Modelscited by 6
  4. 2025Distinguishing Cause from Effect with Causal Velocity Modelscited by 6
  5. 2023Structural restrictions in local causal discovery: identifying direct causes of a target variablecited by 5
  6. 2024Scalable and Flexible Causal Discovery with an Efficient Test for Adjacencycited by 5
  7. 2024Continuous Bayesian Model Selection for Multivariate Causal Discoverycited by 5
  8. 2025Counterfactual Identifiability via Dynamic Optimal Transportcited by 5
  9. 2023Order-based Structure Learning with Normalizing Flowscited by 4
  10. 2025Multi-Domain Causal Discovery in Bijective Causal Modelscited by 4
  11. 2026Causal Representation Learning from General Environments under Nonparametric Mixingcited by 4
  12. 2023Assessing the overall and partial causal well-specification of nonlinear additive noise modelscited by 3
  13. 2023Causal Fair Metric: Bridging Causality, Individual Fairness, and Adversarial Robustnesscited by 3
  14. 2023Learned Causal Method Predictioncited by 3
  15. 2024Causal Bayesian Optimization via Exogenous Distribution Learningcited by 3
  16. 2025Learning Identifiable Structures Helps Avoid Bias in DNN-based Supervised Causal Learningcited by 3
  17. 2025Identifying Causal Direction via Variational Bayesian Compressioncited by 3
  18. 2025Identifying Causal Direction via Dense Functional Classescited by 3
  19. 2025Causal Discovery via Quantile Partial Effectcited by 3
  20. 2025The Relativity of Causal Knowledgecited by 2
  21. 2025Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noisescited by 2
  22. 2025Higher-Order Causal Structure Learning with Additive Modelscited by 2
  23. 2026CDFM: Towards a General-Purpose Causal Discovery Foundation Modelcited by 2
  24. 2026DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanismscited by 2
  25. 2024Enabling Causal Discovery in Post-Nonlinear Models with Normalizing Flowscited by 1
  26. 2025When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discoverycited by 1
  27. 2025Skewness-Robust Causal Discovery in Location-Scale Noise Modelscited by 1
  28. 2026Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approachcited by 1
  29. 2026Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variablescited by 1
  30. 2024Implicit Causal Representation Learning via Switchable Mechanismscited by 0
  31. 2025Principled Input-Output-Conditioned Post-Hoc Uncertainty Estimation for Regression Networkscited by 0
  32. 2025Wasserstein Distributionally Robust Optimization Through the Lens of Structural Causal Models and Individual Fairnesscited by 0
  33. 2025On the Identifiability of Causal Graphs with the Invariance Principlecited by 0
  34. 2025LxCIM: a new rank-based binary classifier performance metric invariant to local exchange of classescited by 0
  35. 2026Sample Complexity of Causal Identification with Temporal Heterogeneitycited by 0
  36. 2026Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Datacited by 0
  37. 2026Auditing Marketing Budget Allocation with Hindsight Regretcited by 0
  38. 2026Counterfactual identifiability beyond global monotonicity: non-monotone triangular structural causal modelscited by 0

50 most cited of 56 All 56 (JSON)