Non-linear Causal Inference using Gaussianity Measures

In this paper we provide theoretical and empirical evidence of a type of asymmetry between causes and effects that is present when these are related via linear models contaminated with additive non-Gaussian noise. This asymmetry is found in the different degrees of Gaussianity of the residuals of linear fits in the causal and the anti-causal direction. More precisely, under certain conditions the distribution of the residuals is closer to a Gaussian distribution when the fit is made in the incorrect or anti-causal direction. The problem of non-linear causal inference is addressed by performing the analysis in an extended feature space. In this space the required computations can be efficiently performed using kernel techniques. The effectiveness of a method based on the asymmetry described is illustrated in a variety of experiments on both synthetic and real-world cause-effect pairs. In the experiments performed one observes the Gaussianization of the residuals if the model is fitted in the anti-causal direction. Furthermore, such a method is competitive with state-of-the-art techniques for causal inference.