Parallel Computing for Bayesian Networks - Bayesian Networks in R: With Applications in Systems Biology - page 116

have been created, a Bayesian network is learned in parallel, independently, from
each split. The corresponding losses can also be computed in parallel and then av-
eraged to produce a cross-validated loss estimate (see Fig. 5.6 ).
Most Bayesian network structure learning algorithms are not explicitly targeted
at classification problems; they seek to minimize the discrepancy between the es-
timated and the true dependence structure rather than classification error. Further-
more, the very concept of a target variable is central in classification but alien to
Bayesian networks, which treat all the variables in the same way. However, there
are some situations in which the classification error, estimated with the prediction
error , may be of interest. For example, the Hailfinder network was designed to fore-
cast severe summer hail in northeastern Colorado. In fact, the nodes whose names
end in Fcst represent the weather conditions in different parts of the region, and
the prediction of their values was the main goal of the original work by Abramson
et al. ( 1996 ).
If we focus on CompPlFcst ( Complete Plains Forecast ), we can see that
Max-Min Hill-Climbing is not able to learn a good classifier.
> bn.cv(hailfinder, 'mmhc', loss = "pred",
+

loss.args = list(target = "CompPlFcst"))

k-fold cross-validation for Bayesian networks

target learning algorithm:

Max-Min Hill-Climbing

number of subsets: 10

loss function:

Classification Error

expected loss: 0.5433

Fig. 5.6 K-fold cross-validation estimation of a loss function for a Bayesian network learning
algorithm