Distinguishing Cause from Effect Using Quantiles: Bivariate Quantile Causal Discovery
This addresses a fundamental problem in causal inference for researchers and practitioners, though it is an incremental improvement with a novel method for a known bottleneck.
The paper tackles the challenge of distinguishing cause from effect in bivariate observational data by developing Bivariate Quantile Causal Discovery (bQCD), a method based on quantile regression and the minimum description length principle, which shows favorable performance compared to state-of-the-art methods in empirical tests.
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.