Learning Bayesian networks from data: Structure optimization and parameter estimation

Bayesian networks have become one of the most prevalent and useful formalisms for representing uncertain knowledge, and have been applied to problems that involve both generative data modeling and discriminative pattern classification. The problem of learning Bayesian networks from data embodies two key sub problems: structure optimization---that is, determining the directed acyclic graph defining the model; and parameter estimation---determining the conditional probability distributions to be associated with each variable. This thesis investigates both the challenges of learning structures and parameters from data. The main contributions of this thesis include: (1) a novel convex optimization algorithm for Bayesian network structure learning; (2) a new globally regularized risk minimization approach for gene regulatory network induction; (3) a new discriminative model selection criterion for score-based structure learning of Bayesian network classifiers; (4) a novel maximum margin discriminative parameter estimation algorithm for learning Bayesian network classifiers; and (5) a novel convex optimization algorithm for Bayesian network parameter learning with hidden variables.