# Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles

arXiv: https://arxiv.org/abs/2507.10767 · HTML: https://mlsanity.com/paper/2507.10767/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 14 Jul 2025.

## Builds on (most cited first, 10 of 10)

- [Learning Linear Non-Gaussian Causal Models in the Presence of Latent Variables](https://mlsanity.com/paper/1908.03932/) (2019)
- [A Discovery Algorithm for Directed Cyclic Graphs](https://mlsanity.com/paper/1302.3599/) (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)
- [Py-Tetrad and RPy-Tetrad: A New Python Interface with R Support for Tetrad Causal Search](https://mlsanity.com/paper/2308.07346/) (2023)
- [Learning Linear Non-Gaussian Polytree Models](https://mlsanity.com/paper/2208.06701/) (2022)
- [Local Causal Discovery with Linear non-Gaussian Cyclic Models](https://mlsanity.com/paper/2403.14843/) (2024)
- [Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding](https://mlsanity.com/paper/2408.04907/) (2024)
- [Learning Linear Non-Gaussian Graphical Models with Multidirected Edges](https://mlsanity.com/paper/2010.05306/) (2020)

## Built on by (most cited first, 3 of 3)

- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Coarsening Linear Non-Gaussian Causal Models with Cycles](https://mlsanity.com/paper/2605.10163/) (2026)
- [The Statistical Cost of Causal Discovery with Feedback](https://mlsanity.com/paper/2609.34050/) (2026)

## Abstract (arXiv)

The paradigm of linear structural equation modeling readily allows one to incorporate causal feedback loops in the model specification. These appear as directed cycles in the common graphical representation of the models. However, the presence of cycles entails difficulties such as the fact that models need no longer be characterized by conditional independence relations. As a result, learning cyclic causal structures remains a challenging problem. In this paper, we offer new insights on this problem in the context of linear non-Gaussian models. First, we precisely characterize when two directed graphs determine the same linear non-Gaussian model. Next, we take up a setting of cycle-disjoint graphs, for which we are able to show that simple quadratic and cubic polynomial relations among low-order moments of a non-Gaussian distribution allow one to locate source cycles. Complementing this with a strategy of decorrelating cycles and multivariate regression allows one to infer a block-topological order among the directed cycles, which leads to a {consistent and computationally efficient algorithm} for learning causal structures with disjoint cycles.