Abstract
We propose an algorithm for learning an optimal Bayesian network from data. Our method is addressed to biological applications, where usually datasets are small but sets of random variables are large. Moreover we assume that there is no need to examine the acyclicity of the graph.
We provide polynomial bounds (with respect to the number of random variables) for time complexity of our algorithm for two generally used scoring criteria: Minimal Description Length and Bayesian-Dirichlet equivalence.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Chickering, D.M.: Learning Bayesian networks is NP-complete. In: Fisher, D., Lenz, H.J. (eds.) Learning from Data: Artificial Inteligence and Statistics V. Springer, Heidelberg (1996)
Chickering, D.M., Heckerman, D., Meek, C.: Large-sample learning of Bayesian networks is NP-hard. Journal of Machine Learning Research 5, 1287–1330 (2004)
Dasgupta, S.: Learning polytrees. In: Proceedings of the 15th Annual Conference on Uncertainty in Artificial Intelligence (UAI 1999), pp. 134–141. Morgan Kaufmann Publishers, San Francisco (1999)
Meek, C.: Finding a path is harder than finding a tree. J. Artificial Intelligence Res. 15, 383–389 (2001) (electronic)
Ott, S., Imoto, S., Miyano, S.: Finding optimal models for small gene networks. In: Pac. Symp. Biocomput., pp. 557–567 (2004)
Heckerman, D., Geiger, D., Chickering, D.M.: Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning 20(3), 197–243 (1995)
Neapolitan, R.E.: Learning Bayesian Networks. Prentice-Hall, Englewood Cliffs (2003)
Friedman, N., Murphy, K., Russell, S.: Learning the structure of dynamic probabilistic networks. In: Cooper, G.F., Moral, S. (eds.) Proceedings of the Fourteenth Conference on Uncertainty in Artificial Inteligence, pp. 139–147 (1998)
Lam, W., Bacchus, F.: Learning Bayesian belief networks: An approach based on the MDL principle. Computational Intelligence 10(3), 269–293 (1994)
Cooper, G.F., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Machine Learning 9, 309–347 (1992)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dojer, N. (2006). Learning Bayesian Networks Does Not Have to Be NP-Hard. In: Královič, R., Urzyczyn, P. (eds) Mathematical Foundations of Computer Science 2006. MFCS 2006. Lecture Notes in Computer Science, vol 4162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11821069_27
Download citation
DOI: https://doi.org/10.1007/11821069_27
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37791-7
Online ISBN: 978-3-540-37793-1
eBook Packages: Computer ScienceComputer Science (R0)