Non-linear Causal Inference using Gaussianity Measures

TL;DR

This paper introduces a novel approach for non-linear causal inference by exploiting asymmetries in Gaussianity of residuals in expanded feature spaces, supported by theoretical insights and empirical validation.

Contribution

It presents a new method leveraging Gaussianity measures in feature space to distinguish causes from effects in non-linear models, demonstrating competitive performance.

Findings

Residuals in the anti-causal direction are more Gaussian.

The method effectively discriminates causes from effects.

It outperforms some existing causal inference techniques.

Abstract

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.