mlsanityData to 7 Oct 2026

A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery

arXiv 2410.06407 ↗First posted 8 Oct 2024cs.LG stat.ME stat.MLcited by 7

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Abstract (arXiv)

Real-world data often violates the equal-variance assumption (homoscedasticity), making it essential to account for heteroscedastic noise in causal discovery. In this work, we explore heteroscedastic symmetric noise models (HSNMs), where the effect Y is modeled as Y = f(X) + σ(X)N, with X as the cause and N as independent noise following a symmetric distribution. We introduce a novel criterion for identifying HSNMs based on the skewness of the score (i.e., the gradient of the log density) of the data distribution. This criterion establishes a computationally tractable measurement that is zero in the causal direction but nonzero in the anticausal direction, enabling the causal direction discovery. We extend this skewness-based criterion to the multivariate setting and propose SkewScore, an algorithm that handles heteroscedastic noise without requiring the extraction of exogenous noise. We also conduct a case study on the robustness of SkewScore in a bivariate model with a latent confounder, providing theoretical insights into its performance. Empirical studies further validate the effectiveness of the proposed method.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 27 of its 61 references that are in the map. First posted on arXiv 8 Oct 2024.

Builds on

27 of 61 references.

References · 27

  1. 2019Generative Modeling by Estimating Gradients of the Data Distributioncited by 4,067
  2. 2018DAGs with NO TEARS: Continuous Optimization for Structure Learningcited by 745
  3. 2019Sliced Score Matching: A Scalable Approach to Density and Score Estimationcited by 381
  4. 2013Learning Bayesian Networks: The Combination of Knowledge and Statistical Datacited by 185
  5. 2013CAM: Causal additive models, high-dimensional order search and penalized regressioncited by 175
  6. 2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
  7. 2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
  8. 2022Score matching enables causal discovery of nonlinear additive noise modelscited by 108
  9. 2020Causal Autoregressive Flowscited by 97
  10. 2022Diffusion Models for Causal Discovery via Topological Orderingcited by 64
  11. 2017Gradient Estimators for Implicit Modelscited by 58
  12. 2022On the Identifiability and Estimation of Causal Location-Scale Noise Modelscited by 56
15 more
  1. 2021Learning latent causal graphs via mixture oraclescited by 55
  2. 2022Latent Hierarchical Causal Structure Discovery with Rank Constraintscited by 50
  3. 2018A Spectral Approach to Gradient Estimation for Implicit Distributionscited by 45
  4. 2023Scalable Causal Discovery with Score Matchingcited by 42
  5. 2023Causal Discovery with Score Matching on Additive Models with Arbitrary Noisecited by 41
  6. 2019Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variablescited by 39
  7. 2022Identifying Patient-Specific Root Causes with the Heteroscedastic Noise Modelcited by 38
  8. 2023Structure Learning with Continuous Optimization: A Sober Look and Beyondcited by 34
  9. 2023A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variablescited by 33
  10. 2021Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Biascited by 29
  11. 2023Assumption violations in causal discovery and the robustness of score matchingcited by 28
  12. 2018Causal Inference via Kernel Deviance Measurescited by 22
  13. 2020Nonparametric Score Estimatorscited by 22
  14. 2023Effective Causal Discovery under Identifiable Heteroscedastic Noise Modelcited by 8
  15. 2023Heteroscedastic Causal Structure Learningcited by 6

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 3; 2026: 4.

7 papers.

  1. 2025Identifying Causal Direction via Variational Bayesian Compressioncited by 3
  2. 2025Causal Discovery via Quantile Partial Effectcited by 3
  3. 2026DAG-FM: A Foundation Model for Causal Discovery under Heterogeneous Causal Mechanismscited by 2
  4. 2025Skewness-Robust Causal Discovery in Location-Scale Noise Modelscited by 1
  5. 2026Beyond Additivity: Causal Discovery in Location-Scale Noise Models with Hidden Variablescited by 1
  6. 2026Causal Direction from Convergence Time: Faster Training in the True Causal Directioncited by 0
  7. 2026Moment Matters: Mean and Variance Causal Graph Discovery from Heteroscedastic Observational Datacited by 0