Using Cooperative Coevolution for Data Mining of Bayesian Networks - Advanced Techniques in Knowledge Discovery and Data Mining - page 163

6.3.3 Criticism of the Previous Approaches
As reported in Wong et al.'s work, the EP formulation seems to have a clear
advantage over the GA one. To account for this, we conjecture that the per-
formance gain is largely due to the different choice of genetic operators in
producing the offspring, which, in effect, influences the exploration of search
space. On the one hand, the success of EP readily suggests that sheer muta-
tions, which correspond to adding or removing an edge or the combination
of the two, are good enough for generating new search points. On the other
hand, the crossover operation, which plays an important role in GAs, seems
to be ineffective. The reason is not di cult to understand because the one-
point crossover, in our case, effectively recombines two graphs arbitrarily. In
most cases, this could result in an invalid structure. In this regard, such re-
combination would seem insignificant and offspring do not properly inherit,
which is supposedly the merit of the crossover operator. Although the inten-
tion to exchange information among the population is good, the traditional
one-point crossover fails to achieve the purpose.
Despite the EP approach performs better, we note that it often requires
a long execution time. For instance, to learn a network with 37 nodes from
a given data set of 10,000 cases, MDLEP needs about an hour to find the
solution, 5 which is intolerable for practical use. At closer inspection, we find
that a major cause of its long execution time is that there are much more
worse offspring (comparing an offspring with its parent) produced than bet-
ter offspring on average. From our experience, if the population size is 50,
we would have, on average, fewer than five better offspring produced in each
generation. This implies that most of the mutation operations generate in-
ferior network structures. Hence, we conjecture that MDLEP is not e cient
enough in finding good solutions.
6.4 Proposed Algorithm
It is straightforward to combine the two approaches for various purposes.
In the literature, there are several attempts that show different realizations
of the idea. 6 We propose a new hybrid framework that targets improving
the learning e ciency. In essence, information from dependency analysis is
exploited in the search-and-scoring process so that the searching will be more
e cient.
5 We use 5000 generations as the termination criterion.
6 For instance, the CB algorithm [6.34] employs a search-and-score approach (i.e.,
K2), which takes as input a node ordering given by the network constructed
by a dependency analysis approach. In another scenario, the BENEDICT algo-
rithm [6.35] uses a metric definition that reflects the discrepancy between the
independence assertions implied by the network and the data.