A Multivariate Causal Discovery based on Post-Nonlinear Model

Understanding causal relations of systems is a fundamental problem in science. The study of causal discovery aims to infer the underlying causal structure from uncontrolled observational samples. One major approach is to assume that causal structures follow structural equation models (SEMs), such as the additive noise model (ANM) and the post-nonlinear (PNL) model, and to identify these causal structures by estimating the SEMs. Although the PNL model is the most general SEM for causal discovery, its estimation method has not been well-developed except for the bivariate case. In this paper, we propose a new causal discovery method based on the multivariate PNL model. We extend the bivariate method to estimate multi-cause PNL models and combine it with the iterative sink search scheme used for the ANM. We apply the proposed method to synthetic and real-world causal discovery problems and show its effectiveness.