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Causal inference using observational data is challenging, especially in thebivariate case. Through the minimum description length principle, we link thepostulate of independence between the generating mechanisms of the cause and ofthe effect given the cause to quantile regression. Based on this theory, wedevelop Bivariate Quantile Causal Discovery (bQCD), a new method to distinguishcause from effect assuming no confounding, selection bias or feedback. Becauseit uses multiple quantile levels instead of the conditional mean only, bQCD isadaptive not only to additive, but also to multiplicative or evenlocation-scale generating mechanisms. To illustrate the effectiveness of ourapproach, we perform an extensive empirical comparison on both synthetic andreal datasets. This study shows that bQCD is robust across differentimplementations of the method (i.e., the quantile regression), computationallyefficient, and compares favorably to state-of-the-art methods.

Distinguishing Cause from Effect Using Quantiles: Bivariate Quantile Causal Discovery