# A Transformational Characterization of Equivalent Bayesian Network Structures

arXiv: https://arxiv.org/abs/1302.4938 · HTML: https://mlsanity.com/paper/1302.4938/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Feb 2013.

## Built on by (most cited first, 30 of 41)

- [Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Game](https://mlsanity.com/paper/2102.13647/) (2021)
- [Greedy Relaxations of the Sparsest Permutation Algorithm](https://mlsanity.com/paper/2206.05421/) (2022)
- [Causal Structure Learning: a Combinatorial Perspective](https://mlsanity.com/paper/2206.01152/) (2022)
- [Fast Scalable and Accurate Discovery of DAGs Using the Best Order Score Search and Grow-Shrink Trees](https://mlsanity.com/paper/2310.17679/) (2023)
- [Learning nonparametric latent causal graphs with unknown interventions](https://mlsanity.com/paper/2306.02899/) (2023)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Verification and search algorithms for causal DAGs](https://mlsanity.com/paper/2206.15374/) (2022)
- [Causal Discovery with Fewer Conditional Independence Tests](https://mlsanity.com/paper/2406.01823/) (2024)
- [Characterization and Greedy Learning of Gaussian Structural Causal Models under Unknown Interventions](https://mlsanity.com/paper/2211.14897/) (2022)
- [Subset verification and search algorithms for causal DAGs](https://mlsanity.com/paper/2301.03180/) (2023)
- [The Causal Chambers: Real Physical Systems as a Testbed for AI Methodology](https://mlsanity.com/paper/2404.11341/) (2024)
- [Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithms](https://mlsanity.com/paper/2107.03863/) (2021)
- [Active causal structure learning with advice](https://mlsanity.com/paper/2305.19588/) (2023)
- [Efficient Enumeration of Markov Equivalent DAGs](https://mlsanity.com/paper/2301.12212/) (2023)
- [A Transformational Characterization of Unconditionally Equivalent Bayesian Networks](https://mlsanity.com/paper/2203.00521/) (2022)
- [Distributional Equivalence in Linear Non-Gaussian Latent-Variable Cyclic Causal Models: Characterization and Learning](https://mlsanity.com/paper/2603.04780/) (2026)
- [New metrics and search algorithms for weighted causal DAGs](https://mlsanity.com/paper/2305.04445/) (2023)
- [Meek Separators and Their Applications in Targeted Causal Discovery](https://mlsanity.com/paper/2310.20075/) (2023)
- [Dynamic Causal Structure Discovery and Causal Effect Estimation](https://mlsanity.com/paper/2501.06534/) (2025)
- [Universal Lower Bound for Learning Causal DAGs with Atomic Interventions](https://mlsanity.com/paper/2111.05070/) (2021)
- [Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGs](https://mlsanity.com/paper/2310.05655/) (2023)
- [Bayesian causal discovery from unknown general interventions](https://mlsanity.com/paper/2312.00509/) (2023)
- [Causal Discovery under Off-Target Interventions](https://mlsanity.com/paper/2402.08229/) (2024)
- [Higher-Order Causal Structure Learning with Additive Models](https://mlsanity.com/paper/2511.03831/) (2025)
- [Causal Razors](https://mlsanity.com/paper/2302.10331/) (2023)
- [Practical Algorithms for Orientations of Partially Directed Graphical Models](https://mlsanity.com/paper/2302.14386/) (2023)
- [A Fixed-Parameter Tractable Algorithm for Counting Markov Equivalence Classes with the same Skeleton](https://mlsanity.com/paper/2310.04218/) (2023)
- [Extracting the Multiscale Causal Backbone of Brain Dynamics](https://mlsanity.com/paper/2311.00118/) (2023)
- [Quotient Normalized Maximum Likelihood Criterion for Learning Bayesian Network Structures](https://mlsanity.com/paper/2408.14935/) (2024)
- [Heterogeneous Causal Discovery of Repeated Undesirable Health Outcomes](https://mlsanity.com/paper/2503.11477/) (2025)

## Abstract (arXiv)

We present a simple characterization of equivalent Bayesian network structures based on local transformations. The significance of the characterization is twofold. First, we are able to easily prove several new invariant properties of theoretical interest for equivalent structures. Second, we use the characterization to derive an efficient algorithm that identifies all of the compelled edges in a structure. Compelled edge identification is of particular importance for learning Bayesian network structures from data because these edges indicate causal relationships when certain assumptions hold.