Structure EM Algorithm for Bayesian Network Learning

This article explores the application of the Expectation-Maximization (EM) algorithm in Bayesian network structure learning. The EM algorithm is an iterative computational method used to estimate model parameters when dealing with observed data and latent variable models. The algorithm alternates between two steps: the E-step (Expectation) computes the expected value of latent variables given current parameters, while the M-step (Maximization) updates parameters to maximize the expected log-likelihood. Bayesian network structure learning involves constructing directed acyclic graphs (DAGs) that represent probabilistic dependencies among variables. When applying the EM algorithm to Bayesian network structure learning, practitioners typically implement parameter estimation using functions like expectation_step() and maximization_step(), while structure search employs score-based methods such as Bayesian Information Criterion (BIC) calculations. This integrated approach enables effective inference of both model parameters and network topology, thereby facilitating accurate modeling and prediction of complex dependency relationships among variables through probabilistic graphical representations.