Parallel Computing for Bayesian Networks - Bayesian Networks in R: With Applications in Systems Biology - page 118

user system elapsed
0.440 0.036 13.007
> stopCluster(cl)
In fact, cross-validation can be used to evaluate any combination of structure
learning algorithms, parameter learning methods, and the respective tuning param-
eters. It can also be used to evaluate a predetermined network structure; in this case,
X ∗ − 1 ,...,

X ∗ − k are used only for parameter learning. Consider, for instance, the naive
Bayes classifier ( Borgelt et al. , 2009 ), which is equivalent to a star-shaped network
with the training variable at the center and all the arcs pointing to the training vari-
able.
> naive = naive.bayes(training = "CompPlFcst",
+ data = hailfinder)
> bn.cv(hailfinder, naive, loss = "pred")

k-fold cross-validation for Bayesian networks

target network structure:
[Naive Bayes Classifier]
number of subsets: 10

loss function:

Classification Error
training node: CompPlFcst
expected loss: 0
As expected, the classification error is considerably lower than with hc or tabu .
Naive Bayes is, despite its simple structure and strong assumptions, one of the most
efficient and effective algorithms in data mining and classification ( Zhang , 2004 ).
The performance gain from the use of a snow cluster is not as marked as in the
previous example (the execution time halves with two slaves, but does not improve
beyond that). This difference in behavior suggests that most of the execution time
in the previous example was spent learning the structure of the network and that, as
anticipated in Sect. 5.3.4 , parameter learning is relatively fast in comparison.

5.4.3 Conditional Probability Queries

Conditional probability queries are the most common form of Bayesian network
inference; as a result, parallel implementations of the exact and approximate algo-
rithms covered in Sect. 4.1.2 have been investigated in literature. Particle filters algo-
rithms, in particular, exhibit coarse-grained parallelism if particles are generated us-
ing Markov chain Monte Carlo approaches or are embarrassingly parallel if particles
are independent. Logic sampling, illustrated in Algorithm 4.2 , falls in the second
category.
Consider, for example, how the knowledge that there is a weather instability in
the mountains (i.e., InsInMt == "Strong" ) and that there is a marked cloud