Target Discovery and Validation Reviews and Protocols

40 Imoto et al.
Fig. 5. Result of the identification of the drug-affected genes (12).
3.2. Bayesian Networks for Exploring Druggable Genes
3.2.1. Introduction of Bayesian Networks
Bayesian networks are a mathematical model for representing complex
phenomena among a large number of random variables by using the joint
probability. In Bayesian networks, the dependency of the random variables is
represented by the dag encoding the Markov assumption between nodes. That
is, the state of a node only depends on its direct parents. Mathematically, we
have a set of random variables {X 1 ,…,X p }, and we consider a dag G as the
dependency underling among random variables. The joint probability of the
random variables can be decomposed as follows:
P
∏
Pr(X 1 ,...,X p ) = Pr(X j | Pa(X j )),
j=1
where Pa(X j ) is the set of random variables corresponding to the direct parents
of X j in G. Figure 6 is an example of a dag of the random variables
{X 1 ,X 2 ,X 3 ,X 4 }. In this case, we have Pa(X 1 ) = {X 2 ,X 3 }, Pa(X 2 ) = , Pa(X 3 ) = X 4 ,
and Pa(X 4 ) = . Then, the joint probability of these four random variables is
decomposed as:
Pr(X 1 ,…, X 4 ) = Pr(X 1 |X 2 , X 3 )Pr(X 2 )Pr(X 3 |X 4 )Pr(X 4 ).
(1)