The Bayesian Structural EM Algorithm

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.

Appears in Proceedings of the Fourteenth Conference on Uncertainty in Artificial Intelligence (UAI1998)

References in corpus (2)

• Context-Specific Independence in Bayesian Networks
• A Bayesian Approach to Learning Bayesian Networks with Local Structure

Cited by in corpus (25)

• Learning the Structure of Dynamic Probabilistic Networks
• Inferring Parameters and Structure of Latent Variable Models by Variational Bayes
• Dynamic Bayesian Multinets
• Parameter-Free Probabilistic API Mining across GitHub
• Expectation Maximization and Complex Duration Distributions for Continuous Time Bayesian Networks
• Learning Bayesian Networks from Incomplete Data with Stochastic Search Algorithms
• Learning Mixtures of DAG Models
• Learning the Dimensionality of Hidden Variables
• Learning the Structure of Deep Sparse Graphical Models
• Bayesian Information Extraction Network
• The Information Bottleneck EM Algorithm
• Advances in Learning Bayesian Networks of Bounded Treewidth
• Learning Why Things Change: The Difference-Based Causality Learner
• Hard and Soft EM in Bayesian Network Learning from Incomplete Data
• Riffled Independence for Efficient Inference with Partial Rankings
• Exchangeable Variable Models
• Gaussian Mixture Models for Affordance Learning using Bayesian Networks
• A Bayesian Network Model for Interesting Itemsets
• Science Fiction Media Representations of Exoplanets: Portrayals of Changing Astronomical Discoveries
• Efficient Probabilistic Inference with Partial Ranking Queries
• Latent Composite Likelihood Learning for the Structured Canonical Correlation Model
• Context-Specific Likelihood Weighting
• Reasoning about Unforeseen Possibilities During Policy Learning
• Learning Bayesian Networks from Ordinal Data
• Identification of Latent Variables From Graphical Model Residuals