# Estimating large causal polytrees from small samples

arXiv: https://arxiv.org/abs/2209.07028 · HTML: https://mlsanity.com/paper/2209.07028/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 44 references that are in the map.
- First posted on arXiv 15 Sep 2022.

## Builds on (most cited first, 13 of 13)

- [DAGs with NO TEARS: Continuous Optimization for Structure Learning](https://mlsanity.com/paper/1803.01422/) (2018)
- [Causal Discovery with Continuous Additive Noise Models](https://mlsanity.com/paper/1309.6779/) (2013)
- [CAM: Causal additive models, high-dimensional order search and penalized regression](https://mlsanity.com/paper/1310.1533/) (2013)
- [High-dimensional learning of linear causal networks via inverse covariance estimation](https://mlsanity.com/paper/1311.3492/) (2013)
- [High-dimensional consistency in score-based and hybrid structure learning](https://mlsanity.com/paper/1507.02608/) (2015)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [A polynomial-time algorithm for learning nonparametric causal graphs](https://mlsanity.com/paper/2006.11970/) (2020)
- [The Recovery of Causal Poly-Trees from Statistical Data](https://mlsanity.com/paper/1304.2736/) (2013)
- [Efficient Bayesian network structure learning via local Markov boundary search](https://mlsanity.com/paper/2110.06082/) (2021)
- [Structure Learning for Directed Trees](https://mlsanity.com/paper/2108.08871/) (2021)
- [Score-based Causal Learning in Additive Noise Models](https://mlsanity.com/paper/1311.6359/) (2013)
- [SparsityBoost: A New Scoring Function for Learning Bayesian Network Structure](https://mlsanity.com/paper/1309.6820/) (2013)
- [Learning Linear Polytree Structural Equation Models](https://mlsanity.com/paper/2107.10955/) (2021)

## Abstract (arXiv)

We consider the problem of estimating a large causal polytree from a relatively small i.i.d. sample. This is motivated by the problem of determining causal structure when the number of variables is very large compared to the sample size, such as in gene regulatory networks. We give an algorithm that recovers the tree with high accuracy in such settings. The algorithm works under essentially no distributional or modeling assumptions other than some mild non-degeneracy conditions.