Chapter 4 - Learning Bayesian Networks

Abstract

This chapter addresses the problem of learning the parameters from data. It also discusses score-based structure learning and constraint-based structure learning. The method for learning all parameters in a Bayesian network follows readily from the method for learning a single parameter. The chapter presents a method for learning the probability of a binomial variable and extends this method to multinomial variables. It also provides guidelines for articulating the prior beliefs concerning probabilities. The chapter illustrates the constraint-based approach by showing how to learn a directed acyclic graph (DAG) faithful to a probability distribution. Structure learning consists of learning the DAG in a Bayesian network from data. It is necessary to know which DAG satisfies the Markov condition with the probability distribution P that is generating the data. The process of learning such a DAG is called “model selection.” A DAG includes a probability distribution P if the DAG does not entail any conditional independencies that are not in P. In score-based structure learning, a score is assigned to each DAG based on the data such that in the limit. After scoring the DAGs, the score are used, possibly along with prior probabilities, to learn a DAG. The most straightforward score, the Bayesian score, is the probability of the data D given the DAG. Once a DAG is learnt from data, the parameters can be known. The result will be a Bayesian network that can be used to do inference. In the constraint-based approach, a DAG is found for which the Markov condition entails all and only those conditional independencies that are in the probability distribution P of the variables of interest. The chapter applies structure learning to inferring causal influences from data and presents learning packages. It presents examples of learning Bayesian networks and of causal learning.