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A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery
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Proposes a skewness-of-score criterion for identifying heteroscedastic symmetric noise models and the SkewScore order-based causal discovery algorithm, which needs no exogenous-noise extraction.
Problem
Causal discovery when noise is heteroscedastic (non-constant variance), where existing methods need noise extraction, Gaussian likelihoods, or lack guarantees, and latent confounders break independent-noise identifiability.
Approach
Identify the sink node as the variable whose score-function component has zero skewness (cubed score has zero mean) under heteroscedastic symmetric noise; iterate to get a topological order, then prune with CI tests, avoiding exogenous noise extraction.
Key results
- SkewScore consistently outperforms or matches baselines across bivariate, latent-confounded triangular, and multivariate synthetic settings (averaged over 100 runs pairwise, 10 runs multivariate).
- Pairwise HNM baselines such as HOST and LOCI degrade with latent confounders under the GP-sig generator, where SkewScore remains strong.
- In multivariate experiments, SkewScore's advantage grows with dimensionality, while DiffAN degrades as d increases.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use SkewScore instead of competing methods for bivariate HSNM direction discovery | Bivariate HSNMs · Bivariate HSNMs | causal direction accuracy | Mixed |
| Use SkewScore instead of HNM baselines on GP-sig data with a latent confounder | Latent-confounded triangular HSNMs · GP-sig | causal direction accuracy | Helped |
| Use SkewScore instead of competing methods for multivariate HSNM discovery | Multivariate HSNMs · Multivariate HSNMs | topological order divergence | Helped |
| Increase the observed causal effect relative to the latent-confounder effect | SkewScore · Latent-confounded triangular HSNM | causal direction identification | Helped |
Surprising findings
- Linear Gaussian additive models are unidentifiable under the skewness criterion, since the skewness of the score is zero in that case.
Limitations
- Multivariate DAG recovery may yield spurious edges under latent confounders; FCI-style PAG output is suggested as a remedy.
- Theory covers bivariate with one latent confounder; extension to multiple latent confounders is future work.
- Identifiability requires non-trivial skewness; linear Gaussian models are unidentifiable.
Experimental setup
Datasets: synthetic HSNM data (Gaussian and Student-t noise, GP-sig and Sig-abs settings)
Benchmarks: synthetic bivariate HSNM latent-confounded triangular HSNM multivariate synthetic HSNM
Metrics: causal direction accuracy topological order divergence structural Hamming distance
Baselines: HECI LOCI HOST DiffAN NoTEARS DAGMA
Builds on: DiffAN sliced score matching FCI ordering-based causal discovery
Closest papers by meaning
- When Additive Noise Meets Unobserved Mediators: Bivariate Denoising Diffusion for Causal Discovery (NeurIPS 2025 · similarity 0.89)
- Strong and Weak Identifiability of Optimization-based Causal Discovery in Non-linear Additive Noise Models (ICML 2025 · similarity 0.88)
- Bivariate Causal Discovery using Bayesian Model Selection (ICML 2024 · similarity 0.88)
- Effective Causal Discovery under Identifiable Heteroscedastic Noise Model (AAAI 2024 · similarity 0.87)
- Causal Discovery via Transformed Low-Rank Quantile Surfaces (NeurIPS 2026 · similarity 0.87)
- Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises (NeurIPS 2025 · similarity 0.87)
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