Skewness-Robust Causal Discovery in Location-Scale Noise Models

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.