Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach

TL;DR

This paper introduces RDMDL, a novel bivariate causal discovery method based on rate-distortion MDL and information dimension, addressing limitations of existing MDL approaches.

Contribution

It proposes a new way to measure the description length of cause variables using rate-distortion theory and information dimension, improving causal inference accuracy.

Findings

RDMDL achieves competitive results on the Tübingen dataset.

The method effectively estimates cause complexity using rate-distortion principles.

Code and experiments are publicly available for reproducibility.

Abstract

Approaches to bivariate causal discovery based on the minimum description length (MDL) principle approximate the (uncomputable) Kolmogorov complexity of the models in each causal direction, selecting the one with the lower total complexity. The premise is that nature's mechanisms are simpler in their true causal order. Inherently, the description length (complexity) in each direction includes the description of the cause variable and that of the causal mechanism. In this work, we argue that current state-of-the-art MDL-based methods do not correctly address the problem of estimating the description length of the cause variable, effectively leaving the decision to the description length of the causal mechanism. Based on rate-distortion theory, we propose a new way to measure the description length of the cause, corresponding to the minimum rate required to achieve a distortion level representative of the underlying distribution. This distortion level is deduced using rules from histogram-based density estimation, while the rate is computed using the related concept of information dimension, based on an asymptotic approximation. Combining it with a traditional approach for the causal mechanism, we introduce a new bivariate causal discovery method, termed rate-distortion MDL (RDMDL). We show experimentally that RDMDL achieves competitive performance on the T\"ubingen dataset. All the code and experiments are publicly available at github.com/tiagobrogueira/Causal-Discovery-In-Exchangeable-Data.