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Apart from the quality of the final solutions, we observe that CCGA has a
tremendous speedup over MDLEP. In general, the gain is more than ten-fold
(from 10.6 to 26.5). We conjecture that there are two important reasons: (1)
Due to the hybrid framework, the search space is reduced. Therefore, CCGA
uses significantly less MDL metric evaluations (i.e., AME) than MDLEP,
which is crucial because evaluation of the MDL metric is a time-consuming
operation. 12 Despite the fact that less evaluation is made, CCGA is still
effective in finding good solutions. (2) Because CCGA requires much fewer
cycle-repairing operations (only for the collaborative structure S and the
merged best-so-far structure) than MDLEP, it can save time.
Because CCGA executes faster and the results can still be competitive
with that of MDLEP, we conclude that CCGA is more e cient than MDLEP.
6.6 Conclusion
In this chapter, we proposed a new algorithm, CCGA, for learning Bayesian
networks more e ciently. The algorithm was tested on a number of network
learning problems, and good Bayesian networks were obtained. We compared
CCGA with MDLEP and found that CCGA is much more e cient. More-
over, CCGA usually discovers better Bayesian networks. With an e cient
algorithm, it enables us to explore interesting applications of Bayesian net-
works on real-world data-mining problems.
Acknowledgment
This research was supported by the Earmarked Grant LU3012/01E from the
Research Grant Council of the Hong Kong Special Administrative Region.
References
6.1 Jensen, F.V.,An Introduction to Bayesian Network,Unversity College of
London Press, 1996.
6.2Heckerman,D., and Horvitz,E., Inferring informational goals from free-text
queries:ABayesian approach, in Cooper, G. F., and Moral, S. (eds.), Proc.
14th Conference of Uncertainty in Artificial Intelligence, Wisconsin, pp. 230-
7, Morgan Kaufmann, July 1998.
6.3 Heckerman, D.,andWellman, M. P., Bayesian networks, Communications of
the ACM, 38, pp. 27-30, March 1995.
12 In our current implementation, every record needs to be examined once for each
query.
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