Differentiable Causal Discovery Under Heteroscedastic Noise

Abstract

We consider the problem of estimating directed acyclic graphs from observational data. Many studies on functional causal models assume the independence of noise terms. Thus, they suffer from the typical violation of model assumption: heteroscedasticity. Several recent studies have assumed heteroscedastic noise instead of additive noise in data generation, though most of the estimation algorithms are for bivariate data. This study aims to improve the capability of continuous optimization-based methods so that they can handle heteroscedastic noise under multivariate non-linear data with no latent confounders. Numerical experiments on synthetic data and fMRI simulation data show that our estimation algorithm improves the estimation of the causal structure under heteroscedastic noise. We also applied our estimation algorithm to real-world data collected from a ceramic substrate manufacturing process, and the results prove the possibility of using the estimated causal graph to accelerate quality improvement.