Discovery of Causal Additive Models in the Presence of Unobserved Variables
This addresses the problem of causal inference in complex real-world data with hidden variables for researchers in statistics and machine learning, but it is incremental as it builds on existing causal additive models.
The study tackled causal discovery from data with unobserved variables in nonlinear settings, specifically focusing on causal additive models, and showed that while not all causal relationships can be identified, their method avoids incorrect inferences and effectively infers causal structures in simulations.
Causal discovery from data affected by unobserved variables is an important but difficult problem to solve. The effects that unobserved variables have on the relationships between observed variables are more complex in nonlinear cases than in linear cases. In this study, we focus on causal additive models in the presence of unobserved variables. Causal additive models exhibit structural equations that are additive in the variables and error terms. We take into account the presence of not only unobserved common causes but also unobserved intermediate variables. Our theoretical results show that, when the causal relationships are nonlinear and there are unobserved variables, it is not possible to identify all the causal relationships between observed variables through regression and independence tests. However, our theoretical results also show that it is possible to avoid incorrect inferences. We propose a method to identify all the causal relationships that are theoretically possible to identify without being biased by unobserved variables. The empirical results using artificial data and simulated functional magnetic resonance imaging (fMRI) data show that our method effectively infers causal structures in the presence of unobserved variables.