# Learning Directed Acyclic Graphs from Partial Orderings

arXiv: https://arxiv.org/abs/2403.16031 · HTML: https://mlsanity.com/paper/2403.16031/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 56 references that are in the map.
- First posted on arXiv 24 Mar 2024.

## Builds on (most cited first, 17 of 17)

- [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)
- [Causal Inference and Causal Explanation with Background Knowledge](https://mlsanity.com/paper/1302.4972/) (2013)
- [On Causal Discovery with Equal Variance Assumption](https://mlsanity.com/paper/1807.03419/) (2018)
- [Learning linear structural equation models in polynomial time and sample complexity](https://mlsanity.com/paper/1707.04673/) (2017)
- [A simple measure of conditional dependence](https://mlsanity.com/paper/1910.12327/) (2019)
- [High-Dimensional Causal Discovery Under non-Gaussianity](https://mlsanity.com/paper/1803.11273/) (2018)
- [Kernel Partial Correlation Coefficient -- a Measure of Conditional Dependence](https://mlsanity.com/paper/2012.14804/) (2020)
- [Integer Programming for Learning Directed Acyclic Graphs from Continuous Data](https://mlsanity.com/paper/1904.10574/) (2019)
- [Hypothesis Testing in High-Dimensional Regression under the Gaussian Random Design Model: Asymptotic Theory](https://mlsanity.com/paper/1301.4240/) (2013)
- [Generalized Sparse Additive Models](https://mlsanity.com/paper/1903.04641/) (2019)
- [The Reduced PC-Algorithm: Improved Causal Structure Learning in Large Random Networks](https://mlsanity.com/paper/1806.06209/) (2018)
- [Consistent Second-Order Conic Integer Programming for Learning Bayesian Networks](https://mlsanity.com/paper/2005.14346/) (2020)
- [Graph estimation with joint additive models](https://mlsanity.com/paper/1304.4654/) (2013)
- [Directed Graphical Models and Causal Discovery for Zero-Inflated Data](https://mlsanity.com/paper/2004.04150/) (2020)
- [Inferring Regulatory Networks by Combining Perturbation Screens and Steady State Gene Expression Profiles](https://mlsanity.com/paper/1312.0335/) (2013)
- [Nonparametric causal structure learning in high dimensions](https://mlsanity.com/paper/2106.11415/) (2021)

## Built on by (most cited first, 2 of 2)

- [Causal Preference Elicitation](https://mlsanity.com/paper/2602.01483/) (2026)
- [Causal Discovery Should Embrace the Wisdom of the Crowd](https://mlsanity.com/paper/2603.02678/) (2026)

## Abstract (arXiv)

Directed acyclic graphs (DAGs) are commonly used to model causal relationships among random variables. In general, learning the DAG structure is both computationally and statistically challenging. Moreover, without additional information, the direction of edges may not be estimable from observational data. In contrast, given a complete causal ordering of the variables, the problem can be solved efficiently, even in high dimensions. In this paper, we consider the intermediate problem of learning DAGs when a partial causal ordering of variables is available. We propose a general estimation framework for leveraging the partial ordering and present efficient estimation algorithms for low- and high-dimensional problems. The advantages of the proposed framework are illustrated via numerical studies.