Telling Cause from Effect using MDL-based Local and Global Regression

TL;DR

This paper introduces an MDL-based method for causal inference between two variables by comparing description lengths of their functional relations, and presents an efficient algorithm that outperforms existing methods.

Contribution

It proposes a novel MDL-based regression approach for causal inference and introduces Slope, a linear-time algorithm that significantly improves accuracy over prior methods.

Findings

Slope outperforms state-of-the-art methods on synthetic data.

The MDL-based approach effectively infers causal direction.

The method is efficient and applicable to real-world data.

Abstract

We consider the fundamental problem of inferring the causal direction between two univariate numeric random variables $X$ and $Y$ from observational data. The two-variable case is especially difficult to solve since it is not possible to use standard conditional independence tests between the variables. To tackle this problem, we follow an information theoretic approach based on Kolmogorov complexity and use the Minimum Description Length (MDL) principle to provide a practical solution. In particular, we propose a compression scheme to encode local and global functional relations using MDL-based regression. We infer $X$ causes $Y$ in case it is shorter to describe $Y$ as a function of $X$ than the inverse direction. In addition, we introduce Slope, an efficient linear-time algorithm that through thorough empirical evaluation on both synthetic and real world data we show outperforms the state of the art by a wide margin.