# MDL Meets Latent Confounders: LNML-based Causal Discovery

arXiv: https://arxiv.org/abs/2607.04133 · HTML: https://mlsanity.com/paper/2607.04133/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 27 references that are in the map.
- First posted on arXiv 5 Jul 2026.

## Builds on (most cited first, 3 of 3)

- [ParceLiNGAM: A causal ordering method robust against latent confounders](https://mlsanity.com/paper/1303.7410/) (2013)
- [Telling Cause from Effect using MDL-based Local and Global Regression](https://mlsanity.com/paper/1709.08915/) (2017)
- [We Are Not Your Real Parents: Telling Causal from Confounded using MDL](https://mlsanity.com/paper/1901.06950/) (2019)

## Abstract (arXiv)

Causal discovery with nonlinear mechanisms and latent confounders remains challenging. Existing methods often rely on either linear assumptions or causal sufficiency, limiting their applicability. We propose an MDL-based causal discovery framework that explicitly accounts for latent confounders while allowing flexible nonlinear mechanisms by minimizing the luckiness normalized maximum likelihood (LNML) code-length. The causal relationship between each variable pair is determined by selecting the shortest code-length of the causal model, and we introduce the notion of Delta-pseudo-collinearity to identify dependencies induced by latent confounders. Based on these ideas, we develop a greedy algorithm, termed Pseudo-Collinearity Guided Causal Discovery (PCG-CD). Experiments on synthetic and real-world datasets demonstrate that the proposed method accurately recovers directed causal relationships and effectively detects latent confounders.