# Causal Discovery with Latent Confounders Based on Higher-Order Cumulants

arXiv: https://arxiv.org/abs/2305.19582 · HTML: https://mlsanity.com/paper/2305.19582/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 44 references that are in the map.
- First posted on arXiv 31 May 2023.

## Builds on (most cited first, 5 of 5)

- [Causal Inference in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/1302.4983/) (2013)
- [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)

## Built on by (most cited first, 16 of 16)

- [Local Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/2405.16225/) (2024)
- [Causal Effect Identification in LiNGAM Models with Latent Confounders](https://mlsanity.com/paper/2406.02049/) (2024)
- [Gene Regulatory Network Inference in the Presence of Selection Bias and Latent Confounders](https://mlsanity.com/paper/2501.10124/) (2025)
- [Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding](https://mlsanity.com/paper/2408.04907/) (2024)
- [Causal Discovery in Mixtures of Populations](https://mlsanity.com/paper/2311.07454/) (2023)
- [The Robustness of Differentiable Causal Discovery in Misspecified Scenarios](https://mlsanity.com/paper/2510.12503/) (2025)
- [Latent Confounded Causal Discovery via Lie Bracket Geometry](https://mlsanity.com/paper/2606.19610/) (2026)
- [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)
- [OCDB: Revisiting Causal Discovery with a Comprehensive Benchmark and Evaluation Framework](https://mlsanity.com/paper/2406.04598/) (2024)
- [Online Time Series Forecasting with Theoretical Guarantees](https://mlsanity.com/paper/2510.18281/) (2025)
- [Identification of Causal Direction under an Arbitrary Number of Latent Confounders](https://mlsanity.com/paper/2510.22711/) (2025)
- [KarmaTS: A Universal Simulation Platform for Multivariate Time Series with Functional Causal Dynamics](https://mlsanity.com/paper/2511.11357/) (2025)
- [From Local to Cluster: A Unified Framework for Causal Discovery with Latent Variables](https://mlsanity.com/paper/2604.22416/) (2026)
- [Hessian Rank Constraint for Learning Structure of Nonlinear Latent Variable Models](https://mlsanity.com/paper/2609.24241/) (2026)
- [Linear Regression Beyond Covariance: Latent Slope Spectra from Higher-Order Cumulants](https://mlsanity.com/paper/2610.17772/) (2026)

## Abstract (arXiv)

Causal discovery with latent confounders is an important but challenging task in many scientific areas. Despite the success of some overcomplete independent component analysis (OICA) based methods in certain domains, they are computationally expensive and can easily get stuck into local optima. We notice that interestingly, by making use of higher-order cumulants, there exists a closed-form solution to OICA in specific cases, e.g., when the mixing procedure follows the One-Latent-Component structure. In light of the power of the closed-form solution to OICA corresponding to the One-Latent-Component structure, we formulate a way to estimate the mixing matrix using the higher-order cumulants, and further propose the testable One-Latent-Component condition to identify the latent variables and determine causal orders. By iteratively removing the share identified latent components, we successfully extend the results on the One-Latent-Component structure to the Multi-Latent-Component structure and finally provide a practical and asymptotically correct algorithm to learn the causal structure with latent variables. Experimental results illustrate the asymptotic correctness and effectiveness of the proposed method.