Distinguishing Cause from Effect Using Quantiles: Bivariate Quantile Causal Discovery

Natasa Tagasovska, Thibault Vatter

Abstract:

Causal inference using observational data is challenging, especially in the bivariate case. Through
the minimum description length principle, we link
the postulate of independence between the generating mechanisms of the cause and of the effect
given the cause to quantile regression. Based on
this theory, we develop Bivariate Quantile Causal
Discovery (bQCD), a new method to distinguish
cause from effect assuming no confounding, selection bias or feedback. Because it uses multiple
quantile levels instead of the conditional mean
only, bQCD is adaptive not only to additive, but
also to multiplicative or even location-scale generating mechanisms. To illustrate the effectiveness of our approach, we perform an extensive
empirical comparison on both synthetic and real
datasets. This study shows that bQCD is robust
across different implementations of the method
(i.e., the quantile regression), computationally efficient, and compares favorably to state-of-the-art
methods