A skewness-based criterion for addressing heteroscedastic noise in causal discovery
Lin, Yingyu Huang, Yuxing Liu, Wenqin Deng, Haoran Ng, Ignavier Zhang, Kun Gong, Mingming Ma, Yian Huang, Biwei
Lin, Yingyu
Huang, Yuxing
Liu, Wenqin
Deng, Haoran
Ng, Ignavier
Zhang, Kun
Gong, Mingming
Ma, Yian
Huang, Biwei
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Department
Machine Learning
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Conference proceeding
Date
2025
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English
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Abstract
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. © 2025 13th International Conference on Learning Representations, ICLR 2025. All rights reserved.
Citation
Y. Lin et al., “A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery,” International Conference on Representation Learning, vol. 2025, pp. 89283–89310, May 2025
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13th International Conference on Learning Representations, ICLR 2025
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13th International Conference on Learning Representations, ICLR 2025
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Source
13th International Conference on Learning Representations, ICLR 2025
Publisher
International Conference on Learning Representations, ICLR