Data to 7 Oct 2026

Learning Equivalence Classes of Bayesian Networks Structures

arXiv 1302.3566 ↗First posted 13 Feb 2013cs.AI cs.LG stat.MLcited by 75

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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.

Key facts. Cited by 75 papers in the map (data through 7 Oct 2026). First posted on arXiv 13 Feb 2013.

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Citing papers per year: 2021: 14; 2022: 7; 2023: 18; 2024: 13; 2025: 14; 2026: 9.

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2021Beware of the Simulated DAG! Causal Discovery Benchmarks May Be Easy To Gamecited by 159
2021A survey of Bayesian Network structure learningcited by 85
2023Integrating Large Language Model for Improved Causal Discoverycited by 54
2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
2023Discovering Causal Relations and Equations from Datacited by 33
2023A Versatile Causal Discovery Framework to Allow Causally-Related Hidden Variablescited by 33
2024Causal Inference with Large Language Model: A Surveycited by 31
2022Counterfactual Fairness with Partially Known Causal Graphcited by 20
2022Data-Driven Causal Effect Estimation Based on Graphical Causal Modelling: A Surveycited by 19
2024Adjustment Identification Distance: A gadjid for Causal Structure Learningcited by 16
2023Benchmarking and Explaining Large Language Model-based Code Generation: A Causality-Centric Approachcited by 15
2024Large Language Models for Constrained-Based Causal Discoverycited by 15

38 more

2023Case Studies of Causal Discovery from IT Monitoring Time Seriescited by 14
2023AI for IT Operations (AIOps) on Cloud Platforms: Reviews, Opportunities and Challengescited by 13
2021Deconfounded Score Method: Scoring DAGs with Dense Unobserved Confoundingcited by 9
2021Entropy-based Discovery of Summary Causal Graphs in Time Seriescited by 9
2022Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs with Applicationscited by 9
2022A Causal Approach to Detecting Multivariate Time-series Anomalies and Root Causescited by 8
2023Causal Discovery from Time Series with Hybrids of Constraint-Based and Noise-Based Algorithmscited by 8
2023Bootstrap aggregation and confidence measures to improve time series causal discoverycited by 8
2024DCILP: A Distributed Approach for Large-Scale Causal Structure Learningcited by 8
2025Extremely Greedy Equivalence Searchcited by 8
2021Effective and efficient structure learning with pruning and model averaging strategiescited by 7
2024Prompting Strategies for Enabling Large Language Models to Infer Causation from Correlationcited by 7
2025CAUSAL3D: A Comprehensive Benchmark for Causal Learning from Visual Datacited by 7
2021A Local Method for Identifying Causal Relations under Markov Equivalencecited by 6
2023Conditional Independence Testing with Heteroskedastic Data and Applications to Causal Discoverycited by 6
2024Interventional Fairness on Partially Known Causal Graphs: A Constrained Optimization Approachcited by 6
2024Hybrid Top-Down Global Causal Discovery with Local Search for Linear and Nonlinear Additive Noise Modelscited by 5
2024Local Causal Discovery with Background Knowledgecited by 5
2021Accelerating Recursive Partition-Based Causal Structure Learningcited by 4
2021Partitioned hybrid learning of Bayesian network structurescited by 4
2021Marginalizable Density Modelscited by 4
2022The interventional Bayesian Gaussian equivalent score for Bayesian causal inference with unknown soft interventionscited by 4
2023Brain Effective Connectome based on fMRI and DTI Data: Bayesian Causal Learning and Assessmentcited by 4
2024Argumentative Causal Discoverycited by 3
2024Causal Reasoning in Software Quality Assurance: A Systematic Reviewcited by 3
2024Detecting and Measuring Confounding Using Causal Mechanism Shiftscited by 3
2021Scalable Bayesian Network Structure Learning with Splinescited by 2
2023Using causal inference to avoid fallouts in data-driven parametric analysis: a case study in the architecture, engineering, and construction industrycited by 2
2023Causal structure learning with momentum: Sampling distributions over Markov Equivalence Classes of DAGscited by 2
2025DAG DECORation: Continuous Optimization for Structure Learning under Hidden Confoundingcited by 2
2026Dynamic Expert-Guided Model Averaging for Causal Discoverycited by 2
2026Test-Time Learning of Causal Structure from Interventional Datacited by 2
2021Markov Blanket Discovery using Minimum Message Lengthcited by 1
2021Learning Linear Polytree Structural Equation Modelscited by 1
2022Learning Large Causal Structures from Inverse Covariance Matrix via Sparse Matrix Decompositioncited by 1
2023Distinguishing Cause from Effect on Categorical Data: The Uniform Channel Modelcited by 1
2024Towards Automated Causal Discovery: a case study on 5G telecommunication datacited by 1
2024LoSAM: Local Search in Additive Noise Models with Mixed Mechanisms and General Noise for Global Causal Discoverycited by 1

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