Bayesian Network Structure Learning from Limited Datasets through Graph Evolution

  • Alberto Paolo Tonda
  • Evelyne Lutton
  • Romain Reuillon
  • Giovanni Squillero
  • Pierre-Henri Wuillemin
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7244)


Bayesian networks are stochastic models, widely adopted to encode knowledge in several fields. One of the most interesting features of a Bayesian network is the possibility of learning its structure from a set of data, and subsequently use the resulting model to perform new predictions. Structure learning for such models is a NP-hard problem, for which the scientific community developed two main approaches: score-and-search metaheuristics, often evolutionary-based, and dependency-analysis deterministic algorithms, based on stochastic tests. State-of-the-art solutions have been presented in both domains, but all methodologies start from the assumption of having access to large sets of learning data available, often numbering thousands of samples. This is not the case for many real-world applications, especially in the food processing and research industry. This paper proposes an evolutionary approach to the Bayesian structure learning problem, specifically tailored for learning sets of limited size. Falling in the category of score-and-search techniques, the methodology exploits an evolutionary algorithm able to work directly on graph structures, previously used for assembly language generation, and a scoring function based on the Akaike Information Criterion, a well-studied metric of stochastic model performance. Experimental results show that the approach is able to outperform a state-of-the-art dependency-analysis algorithm, providing better models for small datasets.


Evolutionary computation Bayesian network structure learning Bayesian networks Genetic Programming Graph representation 


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  1. 1.
    Robinson, R.: Counting unlabeled acyclic digraphs. In: Little, C. (ed.) Combinatorial Mathematics V. Lecture Notes in Mathematics, vol. 622, pp. 28–43. Springer, Heidelberg (1977), doi:10.1007/BFb0069178CrossRefGoogle Scholar
  2. 2.
    Chickering, D.M., Geiger, D., Heckerman, D.: Learning bayesian networks is np-hard. Technical Report MSR-TR-94-17, Microsoft Research, Redmond, WA, USA (November 1994)Google Scholar
  3. 3.
    Carvalho, A.: A cooperative coevolutionary genetic algorithm for learning bayesian network structures. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation, GECCO 2011, pp. 1131–1138. ACM, New York (2011)CrossRefGoogle Scholar
  4. 4.
    Wong, M.L., Lee, S.Y., Leung, K.S.: Data mining of bayesian networks using cooperative coevolution. Decis. Support Syst. 38, 451–472 (2004)CrossRefGoogle Scholar
  5. 5.
    Barriere, O., Lutton, E., Wuillemin, P.H.: Bayesian network structure learning using cooperative coevolution. In: Genetic and Evolutionary Computation Conference, GECCO 2009 (2009)Google Scholar
  6. 6.
    Wong, M.L., Lam, W., Leung, K.S.: Using evolutionary programming and minimum description length principle for data mining of bayesian networks. IEEE Transactions on Pattern Analysis and Machine Intelligence 21(2), 174–178 (1999)CrossRefGoogle Scholar
  7. 7.
    Fournier, F., Wu, Y., McCall, J., Petrovski, A., Barclay, P.: Application of evolutionary algorithms to learning evolved bayesian network models of rig operations in the gulf of mexico. In: 2010 UK Workshop on Computational Intelligence (UKCI), pp. 1–6 (September 2010)Google Scholar
  8. 8.
    Barrière, O., Lutton, E., Baudrit, C., Sicard, M., Pinaud, B., Perrot, N.: Modeling Human Expertise on a Cheese Ripening Industrial Process Using GP. In: Rudolph, G., Jansen, T., Lucas, S., Poloni, C., Beume, N. (eds.) PPSN 2008. LNCS, vol. 5199, pp. 859–868. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  9. 9.
    Friedman, N., Linial, M., Nachman, I., Pe’er, D.: Using bayesian networks to analyze expression data. In: Proceedings of the Fourth Annual International Conference on Computational Molecular Biology, RECOMB 2000, pp. 127–135. ACM, New York (2000)CrossRefGoogle Scholar
  10. 10.
    Akaike, H.: A new look at the statistical model identification. IEEE Transactions on Automatic Control 19(6), 716–723 (1974)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Cheng, J., Bell, D.A., Liu, W.: An algorithm for bayesian belief network construction from data. In: Proceedings of AI & STAT 1997, pp. 83–90 (1997)Google Scholar
  12. 12.
    Spirtes, P., Glymour, C., Scheines, R.: Causation, Prediction, and Search, 2nd edn. MIT Press Books, vol. 1. The MIT Press (2001)Google Scholar
  13. 13.
    Druzdzel, M.J.: SMILE: Structural modeling, inference, and learning engine and GeNIe: A development environment for graphical decision-theoretic models, pp. 902–903. American Association for Artificial Intelligence (1999)Google Scholar
  14. 14.
    Sanchez, E., Schillaci, M., Squillero, G.: Evolutionary Optimization: the uGP toolkit. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  15. 15.
    SourceForge: Host of μgp3,
  16. 16.
    Koza, J., Poli, R.: Genetic programming. In: Burke, E.K., Kendall, G. (eds.) Search Methodologies, pp. 127–164. Springer, US (2005), doi:10.1007/0-387-28356-0_5Google Scholar
  17. 17.
    Squillero, G.: Microgp - an evolutionary assembly program generator. Genetic Programming and Evolvable Machines 6, 247–263 (2005)CrossRefGoogle Scholar
  18. 18.
    Gandini, S., Ruzzarin, W., Sanchez, E., Squillero, G., Tonda, A.: A framework for automated detection of power-related software errors in industrial verification processes. J. Electron. Test. 26, 689–697 (2010)CrossRefGoogle Scholar
  19. 19.
    Beinlich, I.A., Suermondt, H.J., Chavez, R.M., Cooper, G.F.: The ALARM Monitoring System: A Case Study with Two Probabilistic Inference Techniques for Belief Networks. In: Second European Conference on Artificial Intelligence in Medicine, London, Great Britain, vol. 38, pp. 247–256. Springer, Berlin (1989)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Alberto Paolo Tonda
    • 1
  • Evelyne Lutton
    • 2
  • Romain Reuillon
    • 1
  • Giovanni Squillero
    • 3
  • Pierre-Henri Wuillemin
    • 4
  1. 1.Institut des Systèmes ComplexesParisFrance
  2. 2.INRIA Saclay-Ile-de-France, AVIZ Team LRI - Bâtiment 650Université Paris-SudOrsay CedexFrance
  3. 3.DAUINPolitecnico di TorinoTorinoItaly
  4. 4.LIP6 1 Département DÉSIRParisFrance

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