Bayes Nets

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Bayesian networks [79] are graphical representation for probabilistic relationships among a set of random variables. Given a finite set  of discrete random variables where each variable  may take values from a finite set, denoted by . A Bayesian network is an annotated directed acyclic graph (DAG) G that encodes a joint probability distribution over. The nodes of the graph correspond to the random variables. The links of the graph correspond to the direct influence from one variable to the other. If there is a directed link from variable  to variable , variable  will be a parent of variable . Each node is annotated with a conditional probability distribution (CPD) that represents, where  denotes the parents of  in. The pair (, CPD) encodes the joint distribution. A unique joint probability distribution over  from  is factorized as:

Figure 2 is an example of a Bayesian network from Cooper’s paper [16], which is hypothetically about the medical domain with 5 variables. The corresponding CPDs are in Table 1.