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

arXiv: https://arxiv.org/abs/1709.08915 · HTML: https://mlsanity.com/paper/1709.08915/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Sep 2017.

## Built on by (most cited first, 21 of 21)

- [Causal Reasoning and Large Language Models: Opening a New Frontier for Causality](https://mlsanity.com/paper/2305.00050/) (2023)
- [On the Identifiability and Estimation of Causal Location-Scale Noise Models](https://mlsanity.com/paper/2210.09054/) (2022)
- [Self-Compatibility: Evaluating Causal Discovery without Ground Truth](https://mlsanity.com/paper/2307.09552/) (2023)
- [Causal Discovery in Hawkes Processes by Minimum Description Length](https://mlsanity.com/paper/2206.06124/) (2022)
- [Causal versions of Maximum Entropy and Principle of Insufficient Reason](https://mlsanity.com/paper/2102.03906/) (2021)
- [Ordinal Causal Discovery](https://mlsanity.com/paper/2201.07396/) (2022)
- [Robust Estimation of Causal Heteroscedastic Noise Models](https://mlsanity.com/paper/2312.10102/) (2023)
- [Structural restrictions in local causal discovery: identifying direct causes of a target variable](https://mlsanity.com/paper/2307.16048/) (2023)
- [Reinterpreting causal discovery as the task of predicting unobserved joint statistics](https://mlsanity.com/paper/2305.06894/) (2023)
- [Bivariate Causal Discovery for Categorical Data via Classification with Optimal Label Permutation](https://mlsanity.com/paper/2209.08579/) (2022)
- [Identifying Causal Direction via Variational Bayesian Compression](https://mlsanity.com/paper/2505.07503/) (2025)
- [Identifying Causal Direction via Dense Functional Classes](https://mlsanity.com/paper/2509.00538/) (2025)
- [Density Ratio-based Causal Discovery from Bivariate Continuous-Discrete Data](https://mlsanity.com/paper/2505.08371/) (2025)
- [Skewness-Robust Causal Discovery in Location-Scale Noise Models](https://mlsanity.com/paper/2511.14441/) (2025)
- [Bivariate Causal Discovery Using Rate-Distortion MDL: An Information Dimension Approach](https://mlsanity.com/paper/2604.05829/) (2026)
- [Variation-based Cause Effect Identification](https://mlsanity.com/paper/2211.12016/) (2022)
- [Hybrid Causal Identification and Causal Mechanism Clustering](https://mlsanity.com/paper/2507.21792/) (2025)
- [LxCIM: a new rank-based binary classifier performance metric invariant to local exchange of classes](https://mlsanity.com/paper/2512.10053/) (2025)
- [One Ruler: A Same-Hands Re-Evaluation of Bivariate Causal Direction on Tuebingen, with a Parameter-Free Compression Baseline](https://mlsanity.com/paper/2606.23767/) (2026)
- [MDL Meets Latent Confounders: LNML-based Causal Discovery](https://mlsanity.com/paper/2607.04133/) (2026)
- [Inferring Causal Relations between Two Sequences of Events with Language Models](https://mlsanity.com/paper/2609.39406/) (2026)

## Abstract (arXiv)

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.