# Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding

arXiv: https://arxiv.org/abs/2408.04907 · HTML: https://mlsanity.com/paper/2408.04907/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 18 references that are in the map.
- First posted on arXiv 9 Aug 2024.

## Builds on (most cited first, 6 of 6)

- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [ParceLiNGAM: A causal ordering method robust against latent confounders](https://mlsanity.com/paper/1303.7410/) (2013)
- [Causal Discovery with Unobserved Confounding and non-Gaussian Data](https://mlsanity.com/paper/2007.11131/) (2020)
- [High-Dimensional Causal Discovery Under non-Gaussianity](https://mlsanity.com/paper/1803.11273/) (2018)
- [Causal Discovery with Latent Confounders Based on Higher-Order Cumulants](https://mlsanity.com/paper/2305.19582/) (2023)
- [Large Dimensional Independent Component Analysis: Statistical Optimality and Computational Tractability](https://mlsanity.com/paper/2303.18156/) (2023)

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

- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Cross-validating causal discovery via Leave-One-Variable-Out](https://mlsanity.com/paper/2411.05625/) (2024)
- [Causal Effect Identification in lvLiNGAM from Higher-Order Cumulants](https://mlsanity.com/paper/2506.05202/) (2025)
- [Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles](https://mlsanity.com/paper/2507.10767/) (2025)
- [Causal Effect Identification in Heterogeneous Environments from Higher-Order Moments](https://mlsanity.com/paper/2506.11756/) (2025)
- [Learning Sparsest Linear Causal DAGs with Latent Confounders via Higher-Order Cumulants](https://mlsanity.com/paper/2607.05984/) (2026)

## Abstract (arXiv)

We consider linear non-Gaussian structural equation models that involve latent confounding. In this setting, the causal structure is identifiable, but, in general, it is not possible to identify the specific causal effects. Instead, a finite number of different causal effects result in the same observational distribution. Most existing algorithms for identifying these causal effects use overcomplete independent component analysis (ICA), which often suffers from convergence to local optima. Furthermore, the number of latent variables must be known a priori. To address these issues, we propose an algorithm that operates recursively rather than using overcomplete ICA. The algorithm first infers a source, estimates the effect of the source and its latent parents on their descendants, and then eliminates their influence from the data. For both source identification and effect size estimation, we use rank conditions on matrices formed from higher-order cumulants. We prove asymptotic correctness under the mild assumption that locally, the number of latent variables never exceeds the number of observed variables. Simulation studies demonstrate that our method achieves comparable performance to overcomplete ICA even though it does not know the number of latents in advance.