The Bayesian Structural EM Algorithm

2013/01/30 by Nir Friedman, Friedman, Nir · 5 citations
Computer Science · #AI-based Problem Solving and Planning #Artificial Intelligence (cs.AI) #Bayesian Modeling and Causal Inference #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications

paper · pdf · doi:10.48550/arxiv.1301.7373

openalex publication_date 2013/01/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Context-Specific Independence in Bayesian Networks
• Inference and missing data

Cited by

• Shylock: Causal Discovery in Multivariate Time Series based on Hybrid Constraints
• Learning discrete Bayesian networks with hierarchical Dirichlet shrinkage
• Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transport
• Flow based approach for Dynamic Temporal Causal models with non-Gaussian or Heteroscedastic Noises
• The Information Bottleneck EM Algorithm
• Exchangeable Variable Models

Related

• Improving parameter learning of Bayesian nets from incomplete data
• Learning Bayesian Networks from Incomplete Databases
• Properties of Bayesian Belief Network Learning Algorithms
• Discovering the Hidden Structure of Complex Dynamic Systems
• Using New Data to Refine a Bayesian Network