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

TL;DR

This paper introduces a skewness-based criterion and algorithm called SkewScore for causal discovery in data with heteroscedastic noise, enabling direction identification without explicit noise extraction.

Contribution

It proposes a novel skewness-based criterion for HSNMs and extends it to multivariate cases, providing a practical algorithm for causal discovery under heteroscedastic noise.

Findings

SkewScore accurately identifies causal directions in heteroscedastic data.

The method is robust to latent confounders in bivariate models.

Empirical results validate the effectiveness of the proposed approach.

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.