# Learning Equivalence Classes of Bayesian Networks Structures

arXiv: https://arxiv.org/abs/1302.3566 · HTML: https://mlsanity.com/paper/1302.3566/

## Key facts

- Cited by 77 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Feb 2013.

## Built on by (most cited first, 30 of 77)

- [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)
- [Integrating Large Language Model for Improved Causal Discovery](https://mlsanity.com/paper/2306.16902/) (2023)
- [Causal Discovery from Temporal Data: An Overview and New Perspectives](https://mlsanity.com/paper/2303.10112/) (2023)
- [Discovering Causal Relations and Equations from Data](https://mlsanity.com/paper/2305.13341/) (2023)
- [A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variables](https://mlsanity.com/paper/2312.11001/) (2023)
- [Causal Inference with Large Language Model: A Survey](https://mlsanity.com/paper/2409.09822/) (2024)
- [Counterfactual Fairness with Partially Known Causal Graph](https://mlsanity.com/paper/2205.13972/) (2022)
- [Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Survey](https://mlsanity.com/paper/2208.09590/) (2022)
- [Adjustment Identification Distance: A gadjid for Causal Structure Learning](https://mlsanity.com/paper/2402.08616/) (2024)
- [AI for IT Operations (AIOps) on Cloud Platforms: Reviews, Opportunities and Challenges](https://mlsanity.com/paper/2304.04661/) (2023)
- [Benchmarking and Explaining Large Language Model-based Code Generation: A Causality-Centric Approach](https://mlsanity.com/paper/2310.06680/) (2023)
- [Large Language Models for Constrained-Based Causal Discovery](https://mlsanity.com/paper/2406.07378/) (2024)
- [Case Studies of Causal Discovery from IT Monitoring Time Series](https://mlsanity.com/paper/2307.15678/) (2023)
- [Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confounding](https://mlsanity.com/paper/2103.15106/) (2021)
- [Entropy-based Discovery of Summary Causal Graphs in Time Series](https://mlsanity.com/paper/2105.10381/) (2021)
- [Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs with Applications](https://mlsanity.com/paper/2205.02654/) (2022)
- [A Causal Approach to Detecting Multivariate Time-series Anomalies and Root Causes](https://mlsanity.com/paper/2206.15033/) (2022)
- [Causal Discovery from Time Series with Hybrids of Constraint-Based and Noise-Based Algorithms](https://mlsanity.com/paper/2306.08765/) (2023)
- [Bootstrap aggregation and confidence measures to improve time series causal discovery](https://mlsanity.com/paper/2306.08946/) (2023)
- [DCILP: A Distributed Approach for Large-Scale Causal Structure Learning](https://mlsanity.com/paper/2406.10481/) (2024)
- [Extremely Greedy Equivalence Search](https://mlsanity.com/paper/2502.19551/) (2025)
- [Effective and efficient structure learning with pruning and model averaging strategies](https://mlsanity.com/paper/2112.00398/) (2021)
- [Prompting Strategies for Enabling Large Language Models to Infer Causation from Correlation](https://mlsanity.com/paper/2412.13952/) (2024)
- [CAUSAL3D: A Comprehensive Benchmark for Causal Learning from Visual Data](https://mlsanity.com/paper/2503.04852/) (2025)
- [A Local Method for Identifying Causal Relations under Markov Equivalence](https://mlsanity.com/paper/2102.12685/) (2021)
- [Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discovery](https://mlsanity.com/paper/2306.11498/) (2023)
- [Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approach](https://mlsanity.com/paper/2401.10632/) (2024)
- [Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Models](https://mlsanity.com/paper/2405.14496/) (2024)
- [Local Causal Discovery with Background Knowledge](https://mlsanity.com/paper/2408.07890/) (2024)

## Abstract (arXiv)

Approaches to learning Bayesian networks from data typically combine a scoring function with a heuristic search procedure. Given a Bayesian network structure, many of the scoring functions derived in the literature return a score for the entire equivalence class to which the structure belongs. When using such a scoring function, it is appropriate for the heuristic search algorithm to search over equivalence classes of Bayesian networks as opposed to individual structures. We present the general formulation of a search space for which the states of the search correspond to equivalence classes of structures. Using this space, any one of a number of heuristic search algorithms can easily be applied. We compare greedy search performance in the proposed search space to greedy search performance in a search space for which the states correspond to individual Bayesian network structures.