Stochastic Algorithms for Searching Causal Orderings in Bayesian Networks

  • Luis M. de Campos
  • Juan F. Huete
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 90)


The structure of a Bayesian network depends heavily on the ordering of its variables: given any ordering it is always possible to build a Bayesian network whose arcs are consistent with the initial ordering; however, the topology of the network, and therefore the number of conditional independence relationships that may be explicitly represented can vary greatly from one ordering to another. As a sparse representation is always preferable to a denser representation of the same model, the task of determining the ordering giving rise to the network with minimum number of arcs is important. In this work we propose methods to obtain a good approximation to the optimal ordering, using only partial information. More precisely, we only use conditional independence relationships of order zero and one, and search for the ordering which best preserves this information. The search process will be guided by genetic algorithms and simulated annealing.


Genetic Algorithm Simulated Annealing Bayesian Network Conditional Independence None None 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    S. Acid and L.M. de Campos. Benedict: An algorithm for learning probabilistic belief netwoks. In Proc. of the IPMU-96 Conference, 979 - 984, 1996.Google Scholar
  2. [2]
    N. Ansari and E. Hou. Computational Intelligence for Optimization. Kluwer Academic Publishers, 1997.Google Scholar
  3. [3]
    R. Bouckaert. Optimizing causal orderings for generating dag’s from data. In Proc. of the Eighth Conference on Uncertainty in Artificial Intelligence, 9 - 16, 1992.Google Scholar
  4. [4]
    I. Beinlich, H. Seurmondt, R. Chavez, and G. Cooper. The alarm monitoring system: a case study with two probabilistic inference techniques for belief networks. In Proc. of the Second European Conference on Artificial Intelligence in Medicine, 247 - 256, 1989.Google Scholar
  5. [5]
    L.M. de Campos. Independency relationships and learning algorithms for singly connected networks. Journal of Experimental and Theoretical Artificial Intelligence 10: 511 - 549, 1998.MATHCrossRefGoogle Scholar
  6. [6]
    L.M. de Campos and J.F. Huete. On the use of independence relationships for learning simplified belief networks. International Journal of Intelligent Systems, 12: 495 - 522, 1997.CrossRefGoogle Scholar
  7. [7] Campos and J.F. Huete. A new approach for learning belief networks using independence criteria. International Journal of Approximate Reasoning 24: 11 - 37, 2000.MathSciNetMATHCrossRefGoogle Scholar
  8. [8]
    D. Chickering, D. Geiger, and D. Heckerman. Learning bayesian networks is NP-hard. Technical Report MSR-TR-94-17, Microsoft Research, 1994.Google Scholar
  9. [9]
    G.F. Cooper and E. Herskovits. A bayesian method for the induction of probabilistic networks from data. Machine Learning, 9: 309 - 347, 1992.MATHGoogle Scholar
  10. [10]
    D. Heckerman, D. Geiger, and D.M. Chickering. Learning Bayesian networks: The combination of knowledge and statistical data. Machine Learning, 20: 197243, 1995.Google Scholar
  11. [11]
    J.H. Holland. Adaptation in Natural and Artificial Systems. Ann Arbor, MI: The University of Michigan Press, 1975.Google Scholar
  12. [12]
    P. Larranaga, C.M. Kuijpers, R.H. Murga, and Y. Yurramendi. Learning bayesian network structure by searching for the best ordering with genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics- Part A: Systems and Humans, 26 (4): 487 - 493, 1996.CrossRefGoogle Scholar
  13. [13]
    J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan and Kaufmann, San Mateo, 1988.Google Scholar
  14. [14]
    P. Spirtes, C. Glymour, and R. Scheines. Causation, Prediction and Search. Lecture Notes in Statistics 81. Springer Verlag, New York, 1993.Google Scholar
  15. [15]
    M. Singh and M. Valtorta. Construction of bayesian networks structures from data: A survey and an efficient algorithm. International Journal of Approximate Reasoning, 12: 111 - 131, 1995.MATHCrossRefGoogle Scholar
  16. [16]
    T. Verma and J. Pearl. Equivalence and synthesis of causal models. In Proc. of the Sixth Conference on Uncertainty in Artificial Intelligence, 220-227, Mass, 1990.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Luis M. de Campos
    • 1
  • Juan F. Huete
    • 1
  1. 1.Depto. de Ciencias de la Computación e I.A. E.T.S.I.IUniversidad de GranadaGranadaSpain

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