# The Impact of Variable Ordering on Bayesian Network Structure Learning

arXiv: https://arxiv.org/abs/2206.08952 · HTML: https://mlsanity.com/paper/2206.08952/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 47 references that are in the map.
- First posted on arXiv 17 Jun 2022.

## Builds on (most cited first, 14 of 14)

- [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)
- [Learning Bayesian Networks: The Combination of Knowledge and Statistical Data](https://mlsanity.com/paper/1302.6815/) (2013)
- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [A survey of Bayesian Network structure learning](https://mlsanity.com/paper/2109.11415/) (2021)
- [Large-scale empirical validation of Bayesian Network structure learning algorithms with noisy data](https://mlsanity.com/paper/2005.09020/) (2020)
- [Ordering-Based Causal Structure Learning in the Presence of Latent Variables](https://mlsanity.com/paper/1910.09014/) (2019)
- [Properties of Bayesian Belief Network Learning Algorithms](https://mlsanity.com/paper/1302.6792/) (2013)
- [A hybrid algorithm for Bayesian network structure learning with application to multi-label learning](https://mlsanity.com/paper/1506.05692/) (2015)
- [An Empirical-Bayes Score for Discrete Bayesian Networks](https://mlsanity.com/paper/1605.03884/) (2016)
- [Learning Bayesian networks from demographic and health survey data](https://mlsanity.com/paper/1912.00715/) (2019)
- [Optimizing Causal Orderings for Generating DAGs from Data](https://mlsanity.com/paper/1303.5392/) (2013)
- [The Probabilistic Backbone of Data-Driven Complex Networks: An example in Climate](https://mlsanity.com/paper/1912.03758/) (2019)
- [Learning complex dependency structure of gene regulatory networks from high dimensional micro-array data with Gaussian Bayesian networks](https://mlsanity.com/paper/2106.15365/) (2021)

## Built on by (most cited first, 5 of 5)

- [Causal discovery using dynamically requested knowledge](https://mlsanity.com/paper/2310.11154/) (2023)
- [Stable Structure Learning with HC-Stable and Tabu-Stable Algorithms](https://mlsanity.com/paper/2504.01740/) (2025)
- [Dynamic Expert-Guided Model Averaging for Causal Discovery](https://mlsanity.com/paper/2601.16715/) (2026)
- [Graphical Models for Decision-Making: Integrating Causality and Game Theory](https://mlsanity.com/paper/2504.13210/) (2025)
- [Selecting Optimal Variable Order in Autoregressive Ising Models](https://mlsanity.com/paper/2602.20394/) (2026)

## Abstract (arXiv)

Causal Bayesian Networks provide an important tool for reasoning under uncertainty with potential application to many complex causal systems. Structure learning algorithms that can tell us something about the causal structure of these systems are becoming increasingly important. In the literature, the validity of these algorithms is often tested for sensitivity over varying sample sizes, hyper-parameters, and occasionally objective functions. In this paper, we show that the order in which the variables are read from data can have much greater impact on the accuracy of the algorithm than these factors. Because the variable ordering is arbitrary, any significant effect it has on learnt graph accuracy is concerning, and this raises questions about the validity of the results produced by algorithms that are sensitive to, but have not been assessed against, different variable orderings.