mlsanityData to 14 Oct 2026

The Bayesian Structural EM Algorithm

arXiv 1301.7373 ↗First posted 30 Jan 2013cs.LG cs.AI stat.MLcited by 26

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Abstract (arXiv)

In recent years there has been a flurry of works on learning Bayesian networks from data. One of the hard problems in this area is how to effectively learn the structure of a belief network from incomplete data- that is, in the presence of missing values or hidden variables. In a recent paper, I introduced an algorithm called Structural EM that combines the standard Expectation Maximization (EM) algorithm, which optimizes parameters, with structure search for model selection. That algorithm learns networks based on penalized likelihood scores, which include the BIC/MDL score and various approximations to the Bayesian score. In this paper, I extend Structural EM to deal directly with Bayesian model selection. I prove the convergence of the resulting algorithm and show how to apply it for learning a large class of probabilistic models, including Bayesian networks and some variants thereof.

Key facts. Cited by 26 papers in the map (data through 14 Oct 2026). First posted on arXiv 30 Jan 2013.

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Citing papers per year: 2021: 2; 2022: 5; 2023: 5; 2024: 7; 2025: 4; 2026: 3.

26 papers.

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  1. 2023Causal Discovery from Temporal Data: An Overview and New Perspectivescited by 43
  2. 2022MissDAG: Causal Discovery in the Presence of Missing Data with Continuous Additive Noise Modelscited by 22
  3. 2024Building Expressive and Tractable Probabilistic Generative Models: A Reviewcited by 12
  4. 2023Bayesian Structure Scores for Probabilistic Circuitscited by 7
  5. 2022Learning Latent Structural Causal Modelscited by 5
  6. 2023Temporal-spatial Correlation Attention Network for Clinical Data Analysis in Intensive Care Unitcited by 3
  7. 2024Estimating Causal Effects from Learned Causal Networkscited by 3
  8. 2025Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noisescited by 3
  9. 2022Discovery and density estimation of latent confounders in Bayesian networks with evidence lower boundcited by 2
  10. 2021Context-Specific Likelihood Weightingcited by 1
  11. 2022Causal Discovery from Sparse Time-Series Data Using Echo State Networkcited by 1
  12. 2022Learning Multitask Gaussian Bayesian Networkscited by 1
14 more
  1. 2024Learning Cyclic Causal Models from Incomplete Datacited by 1
  2. 2024Investigating the validity of structure learning algorithms in identifying risk factors for intervention in patients with diabetescited by 1
  3. 2024Learning Staged Trees from Incomplete Datacited by 1
  4. 2024MissNODAG: Differentiable Cyclic Causal Graph Learning from Incomplete Datacited by 1
  5. 2026Stable Blanket with Hidden Variables and Cyclescited by 1
  6. 2026KG-SoftMAP: Soft Knowledge-Graph Priors for Bayesian Network Structure Learning from Sparse Discrete Datacited by 1
  7. 2021Identification of Latent Variables From Graphical Model Residualscited by 0
  8. 2023Context-specific kernel-based hidden Markov model for time series analysiscited by 0
  9. 2023Probabilistic Multi-Dimensional Classificationcited by 0
  10. 2024Gaussian Mixture Models for Affordance Learning using Bayesian Networkscited by 0
  11. 2025Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transportcited by 0
  12. 2025Learning discrete Bayesian networks with hierarchical Dirichlet shrinkagecited by 0
  13. 2025Shylock: Causal Discovery in Multivariate Time Series based on Hybrid Constraintscited by 0
  14. 2026RECLAIM: Cyclic Causal Discovery Amid Measurement Noisecited by 0