Learning Bounded Tree-Width Bayesian Networks via Sampling

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9161)


Learning Bayesian networks with bounded tree-width has attracted much attention recently, because low tree-width allows exact inference to be performed efficiently. Some existing methods [12, 14] tackle the problem by using k-trees to learn the optimal Bayesian network with tree-width up to k. In this paper, we propose a sampling method to efficiently find representative k-trees by introducing an Informative score function to characterize the quality of a k-tree. The proposed algorithm can efficiently learn a Bayesian network with tree-width at most k. Experiment results indicate that our approach is comparable with exact methods, but is much more computationally efficient.


Bayesian network Structure learning Bounded tree-width 



This work is supported in part by the grant N00014-12-1-0868 from the US Office of Navy Research.


  1. 1.
    Arnborg, S., Corneil, D.G., Proskurowski, A.: Complexity of finding embeddings in ak-tree. SIAM J. Algebraic Discrete Methods 8(2), 277–284 (1987)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Bache, K., Lichman, M.: UCI machine learning repository (2013).
  3. 3.
    Berg, J., Järvisalo, M., Malone, B.: Learning optimal bounded treewidth bayesian networks via maximum satisfiability. In: Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, pp. 86–95 (2014)Google Scholar
  4. 4.
    Buntine, W.: Theory refinement on Bayesian networks. In: Proceedings of the 7th Conference on Uncertainty in AI, pp. 52–60 (1991)Google Scholar
  5. 5.
    Caminiti, S., Fusco, E.G., Petreschi, R.: Bijective linear time coding and decoding for k-trees. Theory Comp. Syst. 46(2), 284–300 (2010)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Cooper, G.F., Herskovits, E.: A Bayesian method for the induction of probabilistic networks from data. Mach. Learn. 9(4), 309–347 (1992)MATHGoogle Scholar
  7. 7.
    de Campos, C.P., Ji, Q.: Efficient structure learning of Bayesian networks using constraints. J. Mach. Learn. Res. 12, 663–689 (2011)MathSciNetMATHGoogle Scholar
  8. 8.
    de Campos, C.P., Zeng, Z., Ji, Q.: Structure learning of Bayesian networks using constraints. In: Proceedings of the 26th Annual International Conference on Machine Learning, Montreal, Quebec, Canada, pp. 113–120 (2009)Google Scholar
  9. 9.
    Eaton, D., Murphy, K.: Bayesian structure learning using dynamic programming and MCMC. In: Proceedings of the 23rd Conference on Uncertainty in AI, pp. 101–108 (2007)Google Scholar
  10. 10.
    Elidan, G., Gould, S.: Learning bounded treewidth Bayesian networks. J. Mach. Learn. Res. 9, 2699–2731 (2008)MathSciNetMATHGoogle Scholar
  11. 11.
    Heckerman, D., Geiger, D., Chickering, D.M.: Learning Bayesian networks: the combination of knowledge and statistical data. Mach. Learn. 20(3), 197–243 (1995)MATHGoogle Scholar
  12. 12.
    Korhonen, J.H., Parviainen, P.: Exact learning of bounded tree-width Bayesian networks. In: Proceedings of the 16th International Conference on AI and Statistics. JMLR W&CP, vol. 31, pp. 370–378 (2013)Google Scholar
  13. 13.
    Kwisthout, J.H.P., Bodlaender, H.L., van der Gaag, L.C.: The necessity of bounded treewidth for efficient inference in Bayesian networks. In: Proceedings of the 19th European Conference on AI, pp. 237–242 (2010)Google Scholar
  14. 14.
    Nie, S., Mauá, D.D., de Campos, C.P., Ji, Q.: Advances in learning Bayesian networks of bounded treewidth. In: Advances in Neural Information Processing Systems, pp. 2285–2293 (2014)Google Scholar
  15. 15.
    Parviainen, P., Farahani, H.S., Lagergren, J.: Learning bounded tree-width Bayesian networks using integer linear programming. In: Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics, pp. 751–759 (2014)Google Scholar
  16. 16.
    Patil, H.P.: On the structure of k-trees. J. Comb. Inf. Syst. Sci. 11(2–4), 57–64 (1986)MathSciNetMATHGoogle Scholar
  17. 17.
    Schwarz, G.: Estimating the dimension of a model. Ann. Stat. 6(2), 461–464 (1978)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Electrical, Computer and Systems EngineeringRensselaer Polytechnic InstituteTroyUSA
  2. 2.School of Electronics, Electrical Engineering and Computer ScienceQueen’s University BelfastBelfastNorthern Ireland, UK

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