提出新方法识别因果方向，解决真实数据噪声不均问题。
A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery
- 基于数据得分偏度构建因果判定准则。
- 在因果方向上偏度为零，反向则非零，可判别方向。
- 无需提取外生噪声，适合含潜变量的复杂场景。
真实世界数据常违背等方差假设（同方差性），因此在因果发现中需考虑异方差噪声。本文研究异方差对称噪声模型（HSNM），其中结果变量 $Y$ 被建模为 $Y = f(X) + σ(X)N$，$X$ 为原因，$N$ 为独立且服从对称分布的噪声。我们提出一种基于得分（即对数密度梯度）偏度的新判别准则，该准则在因果方向上为零，在反因果方向上非零，具有计算可处理性，可用于判断因果方向。我们将该准则扩展至多变量情形，提出 SkewScore 算法，可在不提取外生噪声的前提下处理异方差噪声。此外，通过在含有潜共因的双变量模型上的案例研究，提供了算法鲁棒性的理论分析。实证研究进一步验证了所提方法的有效性。
原文摘要 · Abstract (English)
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.
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