Data to 7 Oct 2026

Learning Bayesian Networks: The Combination of Knowledge and Statistical Data

arXiv 1302.6815 ↗First posted 27 Feb 2013cs.AIcited by 185

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Abstract (arXiv)

We describe algorithms for learning Bayesian networks from a combination of user knowledge and statistical data. The algorithms have two components: a scoring metric and a search procedure. The scoring metric takes a network structure, statistical data, and a user's prior knowledge, and returns a score proportional to the posterior probability of the network structure given the data. The search procedure generates networks for evaluation by the scoring metric. Our contributions are threefold. First, we identify two important properties of metrics, which we call event equivalence and parameter modularity. These properties have been mostly ignored, but when combined, greatly simplify the encoding of a user's prior knowledge. In particular, a user can express her knowledge-for the most part-as a single prior Bayesian network for the domain. Second, we describe local search and annealing algorithms to be used in conjunction with scoring metrics. In the special case where each node has at most one parent, we show that heuristic search can be replaced with a polynomial algorithm to identify the networks with the highest score. Third, we describe a methodology for evaluating Bayesian-network learning algorithms. We apply this approach to a comparison of metrics and search procedures.

Key facts. Cited by 185 papers in the map (data through 7 Oct 2026). First posted on arXiv 27 Feb 2013.

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Citing papers per year: 2021: 36; 2022: 33; 2023: 34; 2024: 27; 2025: 28; 2026: 27.

185 papers.

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2021D'ya like DAGs? A Survey on Structure Learning and Causal Discoverycited by 209
2022Bayesian Structure Learning with Generative Flow Networkscited by 153
2022DAGMA: Learning DAGs via M-matrices and a Log-Determinant Acyclicity Characterizationcited by 135
2021DiBS: Differentiable Bayesian Structure Learningcited by 105
2022Amortized Inference for Causal Structure Learningcited by 89
2021A survey of Bayesian Network structure learningcited by 85
2022Learning to Induce Causal Structurecited by 68
2023GFlowNets for AI-Driven Scientific Discoverycited by 63
2023Integrating Large Language Model for Improved Causal Discoverycited by 54
2023Joint Bayesian Inference of Graphical Structure and Parameters with a Single Generative Flow Networkcited by 50
2022Adversarial random forests for density estimation and generative modelingcited by 44
2023A Survey on Causal Reinforcement Learningcited by 43

38 more

2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
2021Learning Neural Causal Models with Active Interventionscited by 40
2022From Statistical to Causal Learningcited by 40
2021The impact of prior knowledge on causal structure learningcited by 35
2021Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Modelscited by 22
2022Differentiable Causal Discovery Under Latent Interventionscited by 21
2021CausalAF: Causal Autoregressive Flow for Safety-Critical Driving Scenario Generationcited by 20
2021Optimally Efficient Sequential Calibration of Binary Classifiers to Minimize Classification Errorcited by 17
2023Exploiting Noise as a Resource for Computation and Learning in Spiking Neural Networkscited by 17
2025Causally Reliable Concept Bottleneck Modelscited by 17
2023Benchmarking and Explaining Large Language Model-based Code Generation: A Causality-Centric Approachcited by 15
2021Integer Programming for Causal Structure Learning in the Presence of Latent Variablescited by 14
2021Efficient Bayesian network structure learning via local Markov boundary searchcited by 14
2022Distributed Learning of Generalized Linear Causal Networkscited by 13
2021Greedy structure learning from data that contain systematic missing valuescited by 12
2024Building Expressive and Tractable Probabilistic Generative Models: A Reviewcited by 12
2024Recursive Causal Discoverycited by 12
2024On the Reliability of Large Language Models for Causal Discoverycited by 12
2021Benchpress: A Scalable and Versatile Workflow for Benchmarking Structure Learning Algorithmscited by 11
2022Neural Graphical Modelscited by 11
2022GFlowCausal: Generative Flow Networks for Causal Discoverycited by 11
2023Bivariate Causal Discovery using Bayesian Model Selectioncited by 11
2021Data-driven discovery of interpretable causal relations for deep learning material laws with uncertainty propagationcited by 10
2021Structure learning in polynomial time: Greedy algorithms, Bregman information, and exponential familiescited by 10
2023Active causal structure learning with advicecited by 10
2023Global Optimality in Bivariate Gradient-based DAG Learningcited by 10
2022Polynomial-Time Algorithms for Counting and Sampling Markov Equivalent DAGs with Applicationscited by 9
2023Copula-based transferable models for synthetic population generationcited by 9
2024bnRep: A repository of Bayesian networks from the academic literaturecited by 9
2021Sensitivity and robustness analysis in Bayesian networks with the bnmonitor R packagecited by 8
2023Logical Entity Representation in Knowledge-Graphs for Differentiable Rule Learningcited by 8
2023Applying Large Language Models for Causal Structure Learning in Non Small Cell Lung Cancercited by 8
2021Effective and efficient structure learning with pruning and model averaging strategiescited by 7
2022Multiscale Causal Structure Learningcited by 7
2022Methods for Recovering Conditional Independence Graphs: A Surveycited by 7
2023Bayesian Structure Scores for Probabilistic Circuitscited by 7
2023Open problems in causal structure learning: A case study of COVID-19 in the UKcited by 7
2024A Skewness-Based Criterion for Addressing Heteroscedastic Noise in Causal Discoverycited by 7

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