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

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.

## Implementation

the R source code (August 2017) by Alexander Marx.

## Related Publications

 Marx, A & Vreeken, J Telling Cause from Effect by MDL-based Local and Global Regression. In: Proceedings of the IEEE International Conference on Data Mining (ICDM'17), IEEE, 2017. (full paper, 9.3% acceptance rate; overall 19.9%)