Rewatching Leon Bottou's talk yesterday, I was reminded of David Lopez-Paz's paper on the subject that I had not mentioned before. I wonder if this work could not be helped with some of the tool developed in advanced matrix/tensor factorization:
Non-linear Causal Inference using Gaussianity Measures by Daniel Hernandez-Lobato, Pablo Morales Mombiela, David Lopez-Paz and Alberto Suarez
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.
The attendant implementation is here.
The Randomized Causation Coefficient - implementation -
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