Abstract
The problem of finding a Bayesian network structure which maximizes a score function is known as Bayesian network structure learning from data. We study this problem in this paper with respect to a decomposable score function. Solving this problem is known to be NP-hard. Several algorithms are proposed to overcome this problem such as hill-climbing, dynamic programming, branch and bound, and so on. We propose a new branch and bound algorithm that tries to find the globally optimal network structure with respect to the score function. It is an any-time algorithm, i.e., if stopped, it gives the best solution found. Some pruning strategies are applied to the proposed algorithm and drastically reduce the search space. The performance of the proposed algorithm is compared with the latest algorithm which showed better performance to the others, within several data sets. We showed that the new algorithm outperforms the previously best one.
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References
Chickering, D.M., Meek, C., Heckerman, D.: Large-sample learning of Bayesian networks is NP-Hard. In: Proceedings of the 19th Annual Conference on Uncertainty in Artificial Intelligence, pp. 124–133. Morgan Kaufmann Publishers, San Francisco (2003)
Chickering, D.M.: Learning Bayesian networks is NP-complete. Learning from Data: Artificial Intelligence and Statistics V, 121–130 (1996)
Buntine, W.: Theory refinement on Bayesian Networks. In: Proceedings of the Seventh Conference on Uncertainty in Artificial intelligence, Los Angeles, pp. 52–60 (1991)
Silander, T., Myllymaki, P.: A Simple Approach for Finding the Globally Optimal Bayesian Network Structure. In: Proceedings of the 22nd Annual Conference on Uncertainty in Artificial Intelligence, pp. 445–452 (2006)
Singh, A.P., Moore, A.W.: Finding Optimal Bayesian Networks by Dynamic Programming. Technical Report, Carnegie Mellon University CALD-05-106 (2005)
Koivisto, M., Sood, K., Chickering, D.M.: Exact Bayesian structure discovery in Bayesian networks. Journal of Machine Learning Research 5, 549–573 (2004)
Campos, C.P., Zeng, Z., Ji, Q.: Structure Learning of Bayesian Networks using Constraints. In: Proceedings of the 26th International Conference on Machine Learning, Canada (2009)
Schwartz, G.: Estimating the dimensions of a model. Annals of Statistics 6, 461–464 (1978)
Cooper, G., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 309–347 (1992)
Hecherman, D., Geiger, D., Chickering, D.M.: Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning 20, 197–243 (1995)
Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19, 716–723 (1974)
Asuncion, A., Newman, D.: UCI machine learning repository, http://archive.ics.uci.edu/ml/datasets.html
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Etminani, K., Naghibzadeh, M., Razavi, A.R. (2010). Globally Optimal Structure Learning of Bayesian Networks from Data. In: Diamantaras, K., Duch, W., Iliadis, L.S. (eds) Artificial Neural Networks – ICANN 2010. ICANN 2010. Lecture Notes in Computer Science, vol 6352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15819-3_14
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DOI: https://doi.org/10.1007/978-3-642-15819-3_14
Publisher Name: Springer, Berlin, Heidelberg
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