Multi-Domain Causal Discovery in Bijective Causal Models
This work addresses causal discovery for researchers in machine learning and statistics, offering a more general framework that is incremental over existing models.
The paper tackles causal discovery in multi-domain settings by assuming invariant causal functions and varying noise distributions, showing that the causal diagram can be discovered under less restrictive functional assumptions using bijective generation mechanisms (BGM). Experiments on synthetic and real-world datasets validate the theoretical findings.
We consider the problem of causal discovery (a.k.a., causal structure learning) in a multi-domain setting. We assume that the causal functions are invariant across the domains, while the distribution of the exogenous noise may vary. Under causal sufficiency (i.e., no confounders exist), we show that the causal diagram can be discovered under less restrictive functional assumptions compared to previous work. What enables causal discovery in this setting is bijective generation mechanisms (BGM), which ensures that the functional relation between the exogenous noise $E$ and the endogenous variable $Y$ is bijective and differentiable in both directions at every level of the cause variable $X = x$. BGM generalizes a variety of models including additive noise model, LiNGAM, post-nonlinear model, and location-scale noise model. Further, we derive a statistical test to find the parents set of the target variable. Experiments on various synthetic and real-world datasets validate our theoretical findings.