A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery
<|reference_start|>A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery: 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 $Y = f(X) + \sigma(X)N$, 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.<|reference_end|>
@article{lin2024a,
    title={A Skewness-Based Criterion for Addressing Heteroscedastic Noise in
  Causal Discovery},
    author={Yingyu Lin, Yuxing Huang, Wenqin Liu, Haoran Deng, Ignavier Ng, Kun
  Zhang, Mingming Gong, Yi-An Ma, Biwei Huang},
    journal={arXiv preprint arXiv:2410.06407},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.06407},
    primaryClass={cs.LG stat.ME stat.ML}
}