Bayesian Networks in the Absence of Temporal Information - Bayesian Networks in R: With Applications in Systems Biology - page 46

The EM algorithm assigned the first 52 students (with the exception of number
45) to belong to group A and the remainder to group B . If we consider once more
the discretized marks dmarks we created in Sect. 2.2.6 and include the latent
variable when learning the structure of the network, we obtain a network structure
completely different from the ones in Fig. 2.6 .
> bn.LAT = hc(cbind(dmarks, LAT = latent))
> bn.LAT

Bayesian network learned via Score-based methods

model:
[MECH][ANL][LAT|MECH:ANL][VECT|LAT][ALG|LAT]
[STAT|LAT]
nodes:

6

arcs: 5

undirected arcs: 0

directed arcs: 5

average markov blanket size: 2.00

average neighbourhood size: 1.67

average branching factor: 0.83

learning algorithm:

Hill-Climbing

score:

Bayesian Information Criterion
penalization coefficient: 2.238668
tests used in the learning procedure: 40
optimized: TRUE

The three network structures learned above are shown in Fig. 2.7 ; the one
including the latent variable, bn.LAT , agrees with the network structure reported in
Edwards ( 2000 ). We can clearly see that any causal relationship we could infer with-
out taking LAT into account would be potentially spurious. In fact, we could even
question the assumption that the data are a random sample from a single population
and have not been manipulated in some way beforehand.

2.5 Applications to Gene Expression Profiles

Static Bayesian networks provide a versatile tool for the analysis of many kinds
of biological data, including (but not limited to) single-nucleotide polymorphism
(SNP) data and gene expression profiles. Following the work of Friedman et al.
( 2000 ), the expression level or the allele frequency of each gene is associated with
one node. In addition, we can include in the network additional nodes denoting other