Searching Optimal Bayesian Network Structure on Constraint Search Space: Super-Structure Approach
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Optimal search on Bayesian network structure is known as an NP-hard problem and the applicability of existing optimal algorithms is limited in small Bayesian networks with 30 nodes or so. To learn larger Bayesian networks from observational data, some heuristic algorithms were used, but only a local optimal structure is found and its accuracy is not high in many cases. In this paper, we review optimal search algorithms in a constraint search space; The skeleton of the learned Bayesian network is a sub-graph of the given undirected graph called super-structure. The introduced optimal search algorithm can learn Bayesian networks with several hundreds of nodes when the degree of super-structure is around four. Numerical experiments indicate that constraint optimal search outperforms state-of-the-art heuristic algorithms in terms of accuracy, even if the super-structure is also learned by data.
KeywordsBayesian networks Structural learning Optimal algorithm Constraint search space Super-structure
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- 3.Imoto, S., Goto, T., Miyano, S.: Estimation of genetic networks and functional structures between genes by using Bayesian network and nonparametric regression. In: Pacific Symposium on Biocomputing, vol. 7, pp. 175–186 (2002)Google Scholar
- 6.Ott, S., Imoto, S., Miyano, S.: Finding optimal models for small gene networks. In: Pacific Symposium on Biocomputing, vol. 9, pp. 557–567 (2004)Google Scholar
- 8.Parviainen, P., Koivisto, M.: Exact structure discovery in Bayesian networks with less space. In: Proceedings of the 25th Conference on Uncertainty in Artificial Intelligence (2009)Google Scholar
- 10.Silander, T., Myllymaki, P.: A simple approach for finding the globally optimal Bayesian network structure. In: Conference on Uncertainty in Artificial Intelligence, pp. 445–452 (2006)Google Scholar
- 11.Singh, A.P., Moore, A.W.: Finding optimal Bayesian networks by dynamic programming. In: Technical report, Carnegie Mellon University (2005)Google Scholar
- 12.Tamada, Y., Imoto, S., Miyano, S.: Parallel algorithm for learning optimal Bayesian network structure (submitted for publication)Google Scholar