Discovery of Causal Additive Models in the Presence of Unobserved Variables

TL;DR

This paper addresses the challenge of causal discovery in nonlinear additive models with unobserved variables, proposing a method to identify all causally inferable relationships despite unobserved confounders.

Contribution

It introduces a theoretical framework and a practical method for identifying causally inferable relationships in additive models with unobserved variables, avoiding incorrect inferences.

Findings

Method effectively infers causal structures with unobserved variables

Theoretical results clarify limits of causal identification in nonlinear models

Empirical tests on artificial and fMRI data validate the approach

Abstract

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.