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. A flexible class of models that is general and identifiable in most cases are location-scale noise models (LSNMs), in which the effect $Y$ is modeled based on its causes $\boldsymbol{X}$ as $Y = f(\boldsymbol{X}) + g(\boldsymbol{X})N$. To facilitate the estimation of these models, a prominent assumption is that the noise variable $N$ follows a symmetric distribution. We show that when $N$ is a skewed random variable, which is likely in real-world domains, such approaches drop in performance. To address this limitation, we propose SkewD, a likelihood-based method for causal discovery under LSNMs with skewed noise, employing a combination of heuristic search and expectation conditional maximization for parameter estimation. SkewD extends the usual normal distribution framework to the skew-normal setting, enabling reliable inference under symmetric and skewed noise. While our main focus is on bivariate cause-effect inference, we further showcase how SkewD can be extended to the multivariate setting.