Nonparametric Quantile-Based Causal Discovery
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Telling cause from effect using observational data is a challenging problem, especially in the bivariate case. Contemporary methods often assume an independence between the cause and the generating mechanism of the effect given the cause. From this postulate, they derive asymmetries to uncover causal relationships. In this work, we propose such an approach, based on the link between Kolmogorov complexity and quantile scoring. We use a nonparametric conditional quantile estimator based on copulas to implement our procedure, thus avoiding restrictive assumptions about the joint distribution between cause and effect. In an extensive study on real and synthetic data, we show that quantile copula causal discovery (QCCD) compares favorably to state-of-the-art methods, while at the same time being computationally efficient and scalable.
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