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

2024-10-08

arXiv.org

AI Summary

Causal direction identification under heteroscedastic symmetric noise models (HSNMs) remains challenging due to the absence of explicit noise assumptions and latent confounding. Method: We propose a skewness-based identifiability criterion: under the true causal direction (X ightarrow Y), the skewness of the score function (i.e., the gradient of the log-density) vanishes; it is nonzero under the anticausal direction. Leveraging this, we design SkewScore—a computationally efficient, noise-agnostic algorithm that directly estimates score-function skewness without explicit noise modeling. Contribution/Results: This is the first work to introduce skewness statistics into HSNM-based causal inference. SkewScore is theoretically identifiable for both multivariate systems and settings with latent confounders, with rigorous identifiability proofs provided. Experiments demonstrate its robustness under heteroscedastic noise and latent confounding, consistently outperforming state-of-the-art baselines.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Addressing heteroscedastic noise in causal discovery
• Identifying causal direction using skewness-based criterion
• Extending criterion to multivariate setting with SkewScore

Innovation

• Skewness-based criterion for heteroscedastic noise
• SkewScore algorithm without exogenous noise extraction
• Multivariate extension for causal direction discovery