# We Are Not Your Real Parents: Telling Causal from Confounded using MDL

arXiv: https://arxiv.org/abs/1901.06950 · HTML: https://mlsanity.com/paper/1901.06950/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jan 2019.

## Built on by (most cited first, 6 of 6)

- [The most likely common cause](https://mlsanity.com/paper/2306.17557/) (2023)
- [Causal Structure Learning for Dynamical Systems with Theoretical Score Analysis](https://mlsanity.com/paper/2512.14361/) (2025)
- [A Consistent Estimator for Confounding Strength](https://mlsanity.com/paper/2211.01903/) (2022)
- [Detection of Unobserved Common Causes based on NML Code in Discrete, Mixed, and Continuous Variables](https://mlsanity.com/paper/2403.06499/) (2024)
- [Information-theoretic signatures of causality in Bayesian networks and hypergraphs](https://mlsanity.com/paper/2512.20552/) (2025)
- [MDL Meets Latent Confounders: LNML-based Causal Discovery](https://mlsanity.com/paper/2607.04133/) (2026)

## Abstract (arXiv)

Given data over variables (X1,...,Xm, Y) we consider the problem of finding out whether X jointly causes Y or whether they are all confounded by an unobserved latent variable Z. To do so, we take an information-theoretic approach based on Kolmogorov complexity. In a nutshell, we follow the postulate that first encoding the true cause, and then the effects given that cause, results in a shorter description than any other encoding of the observed variables. The ideal score is not computable, and hence we have to approximate it. We propose to do so using the Minimum Description Length (MDL) principle. We compare the MDL scores under the models where X causes Y and where there exists a latent variables Z confounding both X and Y and show our scores are consistent. To find potential confounders we propose using latent factor modeling, in particular, probabilistic PCA (PPCA). Empirical evaluation on both synthetic and real-world data shows that our method, CoCa, performs very well -- even when the true generating process of the data is far from the assumptions made by the models we use. Moreover, it is robust as its accuracy goes hand in hand with its confidence.