A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916697221365760 |
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| author | Lin, Yingyu Huang, Yuxing Liu, Wenqin Deng, Haoran Ng, Ignavier Zhang, Kun Gong, Mingming Ma, Yi-An Huang, Biwei |
| author_facet | Lin, Yingyu Huang, Yuxing Liu, Wenqin Deng, Haoran Ng, Ignavier Zhang, Kun Gong, Mingming Ma, Yi-An Huang, Biwei |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2410_06407 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | 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, Yi-An Huang, Biwei Machine Learning Methodology 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. |
| title | A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery |
| topic | Machine Learning Methodology |
| url | https://arxiv.org/abs/2410.06407 |