# Learning linear acyclic causal model including Gaussian noise using ancestral relationships

arXiv: https://arxiv.org/abs/2409.00417 · HTML: https://mlsanity.com/paper/2409.00417/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 37 references that are in the map.
- First posted on arXiv 31 Aug 2024.

## Builds on (most cited first, 8 of 8)

- [Strong Completeness and Faithfulness in Bayesian Networks](https://mlsanity.com/paper/1302.4973/) (2013)
- [A fast PC algorithm for high dimensional causal discovery with multi-core PCs](https://mlsanity.com/paper/1502.02454/) (2015)
- [ParceLiNGAM: A causal ordering method robust against latent confounders](https://mlsanity.com/paper/1303.7410/) (2013)
- [An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation](https://mlsanity.com/paper/1303.5435/) (2013)
- [SADA: A General Framework to Support Robust Causation Discovery with Theoretical Guarantee](https://mlsanity.com/paper/1707.01283/) (2017)
- [Causal Learner: A Toolbox for Causal Structure and Markov Blanket Learning](https://mlsanity.com/paper/2103.06544/) (2021)
- [The Dual PC Algorithm and the Role of Gaussianity for Structure Learning of Bayesian Networks](https://mlsanity.com/paper/2112.09036/) (2021)
- [Learning causal graphs using variable grouping according to ancestral relationship](https://mlsanity.com/paper/2403.14125/) (2024)

## Abstract (arXiv)

This paper discusses algorithms for learning causal DAGs. The PC algorithm makes no assumptions other than the faithfulness to the causal model and can identify only up to the Markov equivalence class. LiNGAM assumes linearity and continuous non-Gaussian disturbances for the causal model, and the causal DAG defining LiNGAM is shown to be fully identifiable. The PC-LiNGAM, a hybrid of the PC algorithm and LiNGAM, can identify up to the distribution-equivalence pattern of a linear causal model, even in the presence of Gaussian disturbances. However, in the worst case, the PC-LiNGAM has factorial time complexity for the number of variables. In this paper, we propose an algorithm for learning the distribution-equivalence patterns of a linear causal model with a lower time complexity than PC-LiNGAM, using the causal ancestor finding algorithm in Maeda and Shimizu, which is generalized to account for Gaussian disturbances.