Causal Discovery with General Non-Linear Relationships Using Non-Linear ICA

We consider the problem of inferring causal relationships between two or more passively observed variables. While the problem of such causal discovery has been extensively studied, especially in the bivariate setting, the majority of current methods assume a linear causal relationship, and the few methods which consider non-linear relations usually make the assumption of additive noise. Here, we propose a framework through which we can perform causal discovery in the presence of general non-linear relationships. The proposed method is based on recent progress in non-linear independent component analysis (ICA) and exploits the non-stationarity of observations in order to recover the underlying sources. We show rigorously that in the case of bivariate causal discovery, such non-linear ICA can be used to infer causal direction via a series of independence tests. We further propose an alternative measure for inferring causal direction based on asymptotic approximations to the likelihood ratio, as well as an extension to multivariate causal discovery. We demonstrate the capabilities of the proposed method via a series of simulation studies and conclude with an application to neuroimaging data.