A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery

• URL: http://arxiv.org/abs/2410.06407v1
• Date: Tue, 8 Oct 2024 22:28:30 GMT
• Title: A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discovery
• Authors: Yingyu Lin, Yuxing Huang, Wenqin Liu, Haoran Deng, Ignavier Ng, Kun Zhang, Mingming Gong, Yi-An Ma, Biwei Huang,
• Abstract summary: We investigate heteroscedastic symmetric noise models (HSNMs) 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. We propose SkewScore, an algorithm that handles heteroscedastic noise without requiring the extraction of external noise.
• Score: 47.36895591886043
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 $Y = f(X) + \sigma(X)N$, 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.

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