# Learning Linear Non-Gaussian Polytree Models

arXiv: https://arxiv.org/abs/2208.06701 · HTML: https://mlsanity.com/paper/2208.06701/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 37 references that are in the map.
- First posted on arXiv 13 Aug 2022.

## Builds on (most cited first, 7 of 7)

- [Structure Learning in Graphical Modeling](https://mlsanity.com/paper/1606.02359/) (2016)
- [High-Dimensional Causal Discovery Under non-Gaussianity](https://mlsanity.com/paper/1803.11273/) (2018)
- [Estimation of High-Dimensional Graphical Models Using Regularized Score Matching](https://mlsanity.com/paper/1507.00433/) (2015)
- [The Recovery of Causal Poly-Trees from Statistical Data](https://mlsanity.com/paper/1304.2736/) (2013)
- [Chow-Liu++: Optimal Prediction-Centric Learning of Tree Ising Models](https://mlsanity.com/paper/2106.03969/) (2021)
- [Structure Learning for Directed Trees](https://mlsanity.com/paper/2108.08871/) (2021)
- [Learning partial correlation graphs and graphical models by covariance queries](https://mlsanity.com/paper/1906.09501/) (2019)

## Built on by (most cited first, 7 of 7)

- [Root Cause Analysis of Outliers with Missing Structural Knowledge](https://mlsanity.com/paper/2406.05014/) (2024)
- [Identification of Causal Structure with Latent Variables Based on Higher Order Cumulants](https://mlsanity.com/paper/2312.11934/) (2023)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [Optimal estimation of Gaussian (poly)trees](https://mlsanity.com/paper/2402.06380/) (2024)
- [Causal Discovery for Linear Non-Gaussian Models with Disjoint Cycles](https://mlsanity.com/paper/2507.10767/) (2025)
- [Coarsening Linear Non-Gaussian Causal Models with Cycles](https://mlsanity.com/paper/2605.10163/) (2026)
- [Learning Linear Gaussian Polytree Models with Interventions](https://mlsanity.com/paper/2311.04636/) (2023)

## Abstract (arXiv)

In the context of graphical causal discovery, we adapt the versatile framework of linear non-Gaussian acyclic models (LiNGAMs) to propose new algorithms to efficiently learn graphs that are polytrees. Our approach combines the Chow--Liu algorithm, which first learns the undirected tree structure, with novel schemes to orient the edges. The orientation schemes assess algebraic relations among moments of the data-generating distribution and are computationally inexpensive. We establish high-dimensional consistency results for our approach and compare different algorithmic versions in numerical experiments.