[2604.05829] Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach

Computer Science > Machine Learning arXiv:2604.05829 (cs) [Submitted on 7 Apr 2026] Title:Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach Authors:Tiago Brogueira, Mário A.T. Figueiredo View a PDF of the paper titled Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach, by Tiago Brogueira and M\'ario A.T. Figueiredo View PDF HTML (experimental) 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 re...