An Introduction to Inference and Learning in Bayesian Networks

Bayesian networks (BNs) are modern tools for modeling phenomena in dynamic and static systems and are used in different subjects such as disease diagnosis, weather forecasting, decision making and clustering. A BN is a graphical-probabilistic model which represents causal relations among random variables and consists of a directed acyclic graph and a set of conditional probabilities. Structure learning and parameter learning are two main subjects in BNs. In this paper, we consider a BN with a known structure and then, by simulate some data, we try to learn structure of the network using two well-known algorithms, namely, PC and $ K_{2} $ algorithms. Then, we learn parameters of the network and derive the maximum likelihood, maximum a posteriori and posterior mean estimates of the corresponding parameters. Furthermore, we compare performance of the estimates using the Kullback-Leibler divergence criteria and finally, utilizing a real data set, we consider the structure and parameter learning tasks to illustrate practical utility of the proposed methods.