  We provide theoretical and empirical evidence for a type of asymmetry between
causes and effects that is present when these are related via linear models
contaminated with additive non-Gaussian noise. Assuming that the causes and the
effects have the same distribution, we show that the distribution of the
residuals of a linear fit in the anti-causal direction is closer to a Gaussian
than the distribution of the residuals in the causal direction. This
Gaussianization effect is characterized by reduction of the magnitude of the
high-order cumulants and by an increment of the differential entropy of the
residuals. The problem of non-linear causal inference is addressed by
performing an embedding in an expanded feature space, in which the relation
between causes and effects can be assumed to be linear. The effectiveness of a
method to discriminate between causes and effects based on this type of
asymmetry is illustrated in a variety of experiments using different measures
of Gaussianity. The proposed method is shown to be competitive with
state-of-the-art techniques for causal inference.
