  We consider the problem of causal discovery (structure learning) from
heterogeneous observational data. Most existing methods assume a homogeneous
sampling scheme, which leads to misleading conclusions when violated in many
applications. To this end, we propose a novel approach that exploits data
heterogeneity to infer possibly cyclic causal structures from causally
insufficient systems. The core idea is to model the direct causal effects as
functions of exogenous covariates that properly explain data heterogeneity. We
investigate structure identifiability properties of the proposed model.
Structure learning is carried out in a fully Bayesian fashion, which provides
natural uncertainty quantification. We demonstrate its utility through
extensive simulations and a real-world application.
