Non-linear Causal Inference using Gaussianity Measures

By Daniel Hernández-Lobato, Pablo Morales-Mombiela, David Lopez-Paz, Alberto Suárez. 2014

23 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistical and Nonlinear Physics

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Citations in the corpus

The Arrow of Time in Multivariate Time Series (2016, background): “Hern´andez-Lobato et al. (2011), Morales-Mombiela et al. (2013) and Hern´andez-Lobato et al. (2014) discuss the derivation and application of Gaussianity measures to detect the direction of causal time series.”
From Dependence to Causation (2016, background): “This chapter contains novel material from (Hernández-Lobato et al., 2016), where cited.”