# Recovering Causal Structures from Low-Order Conditional Independencies

arXiv: https://arxiv.org/abs/2010.02675 · HTML: https://mlsanity.com/paper/2010.02675/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Oct 2020.

## Built on by (most cited first, 6 of 6)

- [Characterization and Learning of Causal Graphs with Small Conditioning Sets](https://mlsanity.com/paper/2301.09028/) (2023)
- [Context-Specific Causal Discovery for Categorical Data Using Staged Trees](https://mlsanity.com/paper/2106.04416/) (2021)
- [Differentiable Constraint-Based Causal Discovery](https://mlsanity.com/paper/2510.22031/) (2025)
- [Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networks](https://mlsanity.com/paper/2210.00822/) (2022)
- [SNAP: Sequential Non-Ancestor Pruning for Targeted Causal Effect Estimation With an Unknown Graph](https://mlsanity.com/paper/2502.07857/) (2025)
- [On Different Notions of Redundancy in Conditional-Independence-Based Discovery of Graphical Models](https://mlsanity.com/paper/2502.08531/) (2025)

## Abstract (arXiv)

One of the common obstacles for learning causal models from data is that high-order conditional independence (CI) relationships between random variables are difficult to estimate. Since CI tests with conditioning sets of low order can be performed accurately even for a small number of observations, a reasonable approach to determine casual structures is to base merely on the low-order CIs. Recent research has confirmed that, e.g. in the case of sparse true causal models, structures learned even from zero- and first-order conditional independencies yield good approximations of the models. However, a challenging task here is to provide methods that faithfully explain a given set of low-order CIs. In this paper, we propose an algorithm which, for a given set of conditional independencies of order less or equal to k, where k is a small fixed number, computes a faithful graphical representation of the given set. Our results complete and generalize the previous work on learning from pairwise marginal independencies. Moreover, they enable to improve upon the 0-1 graph model which, e.g. is heavily used in the estimation of genome networks.