Learning: The Maximum Likelihood Approach

Abstract

We discuss in this chapter the process of learning Bayesian networks from data. The learning process is studied under different conditions, which relate to the nature of available data and the amount of prior knowledge we have on the Bayesian network. Introduction Consider Figure 17.1, which depicts a Bayesian network structure from the domain of medical diagnosis (we treated this network in Chapter 5). Consider also the data set depicted in this figure. Each row in this data set is called a case and represents a medical record for a particular patient. Note that some of the cases are incomplete, where “?” indicates the unavailability of corresponding data for that patient. The data set is therefore said to be incomplete due to these missing values; otherwise, it is called a complete data set. A key objective of this chapter is to provide techniques for estimating the parameters of a network structure given both complete and incomplete data sets. The techniques we provide therefore complement those given in Chapter 5 for constructing Bayesian networks. In particular we can now construct the network structure from either design information or by working with domain experts, as discussed in Chapter 5, and then use the techniques discussed in this chapter to estimate the CPTs of these structures from data. We also discuss techniques for learning the network structure itself, although our focus here is on complete data sets for reasons that we state later.