# ParceLiNGAM: A causal ordering method robust against latent confounders

arXiv: https://arxiv.org/abs/1303.7410 · HTML: https://mlsanity.com/paper/1303.7410/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Mar 2013.

## Built on by (most cited first, 29 of 29)

- [Identifiability of latent-variable and structural-equation models: from linear to nonlinear](https://mlsanity.com/paper/2302.02672/) (2023)
- [Latent Hierarchical Causal Structure Discovery with Rank Constraints](https://mlsanity.com/paper/2210.01798/) (2022)
- [A Survey on Causal Reinforcement Learning](https://mlsanity.com/paper/2302.05209/) (2023)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Causal Discovery with Latent Confounders Based on Higher-Order Cumulants](https://mlsanity.com/paper/2305.19582/) (2023)
- [Generalized Independent Noise Condition for Estimating Causal Structure with Latent Variables](https://mlsanity.com/paper/2308.06718/) (2023)
- [Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants](https://mlsanity.com/paper/2312.11934/) (2023)
- [FRITL: A Hybrid Method for Causal Discovery in the Presence of Latent Confounders](https://mlsanity.com/paper/2103.14238/) (2021)
- [Learning linear non-Gaussian directed acyclic graph with diverging number of nodes](https://mlsanity.com/paper/2111.00740/) (2021)
- [Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding](https://mlsanity.com/paper/2408.04907/) (2024)
- [Causal Additive Models with Unobserved Causal Paths and Backdoor Paths](https://mlsanity.com/paper/2502.07646/) (2025)
- [Causal Discovery in Linear Structural Causal Models with Deterministic Relations](https://mlsanity.com/paper/2111.00341/) (2021)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Latent Confounded Causal Discovery via Lie Bracket Geometry](https://mlsanity.com/paper/2606.19610/) (2026)
- [Causal Order Identification to Address Confounding: Binary Variables](https://mlsanity.com/paper/2108.04947/) (2021)
- [Generalization of LiNGAM that allows confounding](https://mlsanity.com/paper/2401.16661/) (2024)
- [Disentangling Observed Causal Effects from Latent Confounders using Method of Moments](https://mlsanity.com/paper/2101.06614/) (2021)
- [Application of quantum computing to a linear non-Gaussian acyclic model for novel medical knowledge discovery](https://mlsanity.com/paper/2110.04485/) (2021)
- [Recovering Linear Causal Models with Latent Variables via Cholesky Factorization of Covariance Matrix](https://mlsanity.com/paper/2311.00674/) (2023)
- [Controlling for discrete unmeasured confounding in nonlinear causal models](https://mlsanity.com/paper/2408.05647/) (2024)
- [TSLiNGAM: DirectLiNGAM under heavy tails](https://mlsanity.com/paper/2308.05422/) (2023)
- [Recursive Counterfactual Deconfounding for Object Recognition](https://mlsanity.com/paper/2309.13924/) (2023)
- [Detection of Unobserved Common Causes based on NML Code in Discrete, Mixed, and Continuous Variables](https://mlsanity.com/paper/2403.06499/) (2024)
- [Redefining the Shortest Path Problem Formulation of the Linear Non-Gaussian Acyclic Model: Pairwise Likelihood Ratios, Prior Knowledge, and Path Enumeration](https://mlsanity.com/paper/2404.11922/) (2024)
- [Learning linear acyclic causal model including Gaussian noise using ancestral relationships](https://mlsanity.com/paper/2409.00417/) (2024)
- [Addressing pitfalls in implicit unobserved confounding synthesis using explicit block hierarchical ancestral sampling](https://mlsanity.com/paper/2503.09194/) (2025)
- [MDL Meets Latent Confounders: LNML-based Causal Discovery](https://mlsanity.com/paper/2607.04133/) (2026)
- [Learning Sparsest Linear Causal DAGs with Latent Confounders via Higher-Order Cumulants](https://mlsanity.com/paper/2607.05984/) (2026)
- [MARCEDES: Score-based causal discovery under non-Gaussianity with continuous optimization](https://mlsanity.com/paper/2609.30643/) (2026)

## Abstract (arXiv)

We consider learning a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are correct. But, the estimation results could be distorted if some assumptions actually are violated. In this paper, we propose a new algorithm for learning causal orders that is robust against one typical violation of the model assumptions: latent confounders. The key idea is to detect latent confounders by testing independence between estimated external influences and find subsets (parcels) that include variables that are not affected by latent confounders. We demonstrate the effectiveness of our method using artificial data and simulated brain imaging data.