# Learning Linear Gaussian Polytree Models with Interventions

arXiv: https://arxiv.org/abs/2311.04636 · HTML: https://mlsanity.com/paper/2311.04636/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 61 references that are in the map.
- First posted on arXiv 8 Nov 2023.

## Builds on (most cited first, 21 of 21)

- [Differentiable Causal Discovery from Interventional Data](https://mlsanity.com/paper/2007.01754/) (2020)
- [Invariant Causal Prediction for Nonlinear Models](https://mlsanity.com/paper/1706.08576/) (2017)
- [Permutation-based Causal Inference Algorithms with Interventions](https://mlsanity.com/paper/1705.10220/) (2017)
- [Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions](https://mlsanity.com/paper/1802.06310/) (2018)
- [Permutation-Based Causal Structure Learning with Unknown Intervention Targets](https://mlsanity.com/paper/1910.09007/) (2019)
- [A Survey on Causal Discovery: Theory and Practice](https://mlsanity.com/paper/2305.10032/) (2023)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Learning Causal Structures Using Regression Invariance](https://mlsanity.com/paper/1705.09644/) (2017)
- [Recursive Causal Structure Learning in the Presence of Latent Variables and Selection Bias](https://mlsanity.com/paper/2110.12036/) (2021)
- [BaCaDI: Bayesian Causal Discovery with Unknown Interventions](https://mlsanity.com/paper/2206.01665/) (2022)
- [Jointly interventional and observational data: estimation of interventional Markov equivalence classes of directed acyclic graphs](https://mlsanity.com/paper/1303.3216/) (2013)
- [A Recursive Markov Boundary-Based Approach to Causal Structure Learning](https://mlsanity.com/paper/2010.04992/) (2020)
- [The Recovery of Causal Poly-Trees from Statistical Data](https://mlsanity.com/paper/1304.2736/) (2013)
- [Learning Polytrees](https://mlsanity.com/paper/1301.6688/) (2013)
- [Learning Bayesian Networks in the Presence of Structural Side Information](https://mlsanity.com/paper/2112.10884/) (2021)
- [Novel Ordering-based Approaches for Causal Structure Learning in the Presence of Unobserved Variables](https://mlsanity.com/paper/2208.06935/) (2022)
- [Structure Learning for Directed Trees](https://mlsanity.com/paper/2108.08871/) (2021)
- [Learning Linear Non-Gaussian Polytree Models](https://mlsanity.com/paper/2208.06701/) (2022)
- [On the Parameterized Complexity of Polytree Learning](https://mlsanity.com/paper/2105.09675/) (2021)
- [A Fast Non-parametric Approach for Local Causal Structure Learning](https://mlsanity.com/paper/2111.14969/) (2021)
- [The Hellinger Correlation](https://mlsanity.com/paper/1810.10276/) (2018)

## Abstract (arXiv)

We present a consistent and highly scalable local approach to learn the causal structure of a linear Gaussian polytree using data from interventional experiments with known intervention targets. Our methods first learn the skeleton of the polytree and then orient its edges. The output is a CPDAG representing the interventional equivalence class of the polytree of the true underlying distribution. The skeleton and orientation recovery procedures we use rely on second order statistics and low-dimensional marginal distributions. We assess the performance of our methods under different scenarios in synthetic data sets and apply our algorithm to learn a polytree in a gene expression interventional data set. Our simulation studies demonstrate that our approach is fast, has good accuracy in terms of structural Hamming distance, and handles problems with thousands of nodes.