Skewness-Robust Causal Discovery in Location-Scale Noise Models

TL;DR

This paper introduces SkewD, a likelihood-based algorithm for causal discovery in location-scale noise models that effectively handles skewed noise distributions, improving reliability over traditional methods.

Contribution

The paper proposes SkewD, extending causal discovery methods to skew-normal noise, enhancing robustness and accuracy in real-world skewed data scenarios.

Findings

SkewD outperforms existing methods on skewed noise datasets.

SkewD remains robust under high skewness levels.

Experimental results show improved causal inference accuracy.

Abstract

To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. Crucially, we need to be able to distinguish cause $X$ from effect $Y$ in bivariate models, that is, distinguish the two graphs $X \to Y$ and $Y \to X$. Location-scale noise models (LSNMs), in which the effect $Y$ is modeled based on the cause $X$ as $Y = f(X) + g(X)N$, form a flexible class of models that is general and identifiable in most cases. Estimating these models for arbitrary noise terms $N$, however, is challenging. Therefore, practical estimators are typically restricted to symmetric distributions, such as the normal distribution. As we showcase in this paper, when $N$ is a skewed random variable, which is likely in real-world domains, the reliability of these approaches decreases. To approach this limitation, we propose SkewD, a likelihood-based algorithm for bivariate causal discovery under LSNMs with skewed noise distributions. SkewD extends the usual normal-distribution framework to the skew-normal setting, enabling reliable inference under symmetric and skewed noise. For parameter estimation, we employ a combination of a heuristic search and an expectation conditional maximization algorithm. We evaluate SkewD on novel synthetically generated datasets with skewed noise as well as established benchmark datasets. Throughout our experiments, SkewD exhibits a strong performance and, in comparison to prior work, remains robust under high skewness.