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Partial Abductive Inference in Bayesian Networks: An Empirical Comparison Between GAs and EDAs

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Estimation of Distribution Algorithms

Part of the book series: Genetic Algorithms and Evolutionary Computation ((GENA,volume 2))

Abstract

Partial abductive inference in Bayesian networks is intended as the pro-cess of generating the K most probable configurations for a distinguished subset of the network variables (explanation set), given some observations (evidence). This problem, also known as the Maximum a Posteriori Problem, is known to be NP-hard, so exact computation is not always possible. As partial abductive inference in Bayesian networks can be viewed as a combinatorial optimization problem, Genetic Algorithms have been successfully applied to give an approximate algorithm for it (de Campos et al., 1999). In this work we approach the problem by means of Estimation of Distribution Algorithms, and an empirical comparison between the results obtained by Genetic Algorithms and Estimation of Distribution Algorithms is carried out.

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References

  • Beinlich, I.A., Suermondt, H.J., Chavez, R.M., and Cooper, G.F. (1989). The ALARM monitoring system: A case study with two probabilistic inference techniques for belief networks. In Proceedings of the Second European Conference on Artificial Intelligence in Medicine, pages 247–256. Springer-Verlag.

    Google Scholar 

  • Cano, A. and Moral, S. (1996). A genetic algorithm to approximate convex sets of probabilities. In Procceedings of the 6th International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU’96), pages 847–852.

    Google Scholar 

  • Cooper, G.F. (1990). Probabilistic inference using belief networks is NP-hard. Artificial Intelligence, 42(2–3):393–405.

    Article  MathSciNet  MATH  Google Scholar 

  • Dawid, A.P. (1992). Applications of a general propagation algorithm for probabilistic expert systems. Statistics and Computing, 2:25–36.

    Article  Google Scholar 

  • De Bonet J.S., Isbell, C.L., and Viola, P. (1997). MIMIC: Finding optima by estimating probability densities. Advances in Neural Information Processing. Systems, Vol. 9.

    Google Scholar 

  • de Campos, L.M., Gámez, J.A., and Moral, S. (1999). Partial Abductive Inference in Bayesian Belief Networks using a Genetic Algorithm. Pattern Recognition Letters, 20(11–13):1211–1217.

    Article  Google Scholar 

  • de Campos, L.M., Gámez, J.A., and Moral, S. (2000). On the problem of performing exact partial abductive inference in Bayesian belief networks using junction trees. In Proceedings of the 8th International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU’00), pages 1270–1277.

    Google Scholar 

  • de Campos, L.M. and Huete, J.F. (2000). Approximating causal orderings for Bayesian networks using genetic algorithms and simulated annealing. In 8th International Conference on Information Processing and Management of Uncertainty in Knowledge-based Systems (IPMU’00), pages 333–340.

    Google Scholar 

  • Etxeberria, R. and Larrañaga, P. (1999). Global optimization with Bayesian networks. In II Symposium on Artificial Intelligence. CIMAF99. Special Session on Distributions and Evolutionary Optimization, pages 332–339.

    Google Scholar 

  • Gelsema, E.S. (1995). Abductive reasoning in Bayesian belief networks using a genetic algorithm. Pattern Recognition Letters, 16:865–871.

    Article  Google Scholar 

  • Jensen, F.V. (1996). An introduction to Bayesian Networks. UCL Press. Jensen, F.V., Lauritzen, S.L., and Olesen, K.G. (1990). Bayesian updating in causal probabilistic networks by local computation. Computational Statistics Quarterly, 4:269–282.

    Google Scholar 

  • Larranaga, P., Kuijpers, C., Murga, R., and Y. Yurramendi (1996a). Learning Bayesian network structures by searching for the best ordering with genetic algorithms. IEEE Transactions on System, Man and Cybernetics, 26(4):487–493.

    Article  Google Scholar 

  • Larranaga, P., Kuijpers, C., Poza, M., and Murga, R. (1997). Decomposing Bayesian networks: triangulation of the moral graph with genetic algorithms. Statistics and Computing, 7:19–34.

    Article  Google Scholar 

  • Larranaga, P., Poza, M., Yurramendi, Y., Murga, R., and Kuijpers, C. (1996b). Structure learning of Bayesian networks by genetic algorithms. A perfomance analysis of control parameters. IEEE Transactions on Pattern Analysis and Machine Intelligence, 18(9):912–926.

    Article  Google Scholar 

  • Lauritzen, S.L. and Spiegelhalter, D.J. (1988). Local computations with probabilities on graphical structures and their application to expert systems. J.R. Statistics Society. Serie B, 50(2):157–224.

    MathSciNet  MATH  Google Scholar 

  • Michalewicz, Z. (1996). Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag.

    MATH  Google Scholar 

  • Mühlenbein, H.M. (1998). The equation for response to selection and its use for prediction. Evolutionary Computation, 5:303–346.

    Article  Google Scholar 

  • Neapolitan, R.E. (1990). Probabilistic Reasoning in Expert Systems. Theory and Algorithms. Wiley Interscience.

    Google Scholar 

  • Nilsson, D. (1998). An efficient algorithm for finding the M most probable configurations in Bayesian networks. Statistics and Computing, 2:159–173.

    Article  Google Scholar 

  • Pearl, J. (1987). Distributed revision of composite beliefs. Artificial Intelligence, 33:173–215.

    Article  MathSciNet  MATH  Google Scholar 

  • Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems. Morgan Kaufmann.

    Google Scholar 

  • Rojas-Guzman, C. and Kramer, M.A. (1996). An evolutionary computing approach to probabilistic reasoning in Bayesian networks. Evolutionary Computation, 4:57–85.

    Article  Google Scholar 

  • Seroussi, B. and Goldmard, J.L. (1994). An algorithm directly finding the K most probable configurations in Bayesian networks. International Journal of Approximate Reasoning, 11:205–233.

    Article  Google Scholar 

  • Shafer, G.R. (1996). Probabilistic Expert Systems. Society for Industrial and Applied Mathematics (SIAM).

    Google Scholar 

  • Shenoy, P.P. and Shafer, G.R. (1990). Axioms for probability and belief-function propagation. In Shachter, R., Levitt, T., Kanal, L., and Lemmer, J., editors, Uncertainty in Artificial Intelligence, 4, 169–198. Elsevier Science Publishers B.V. (North-Holland).

    MathSciNet  Google Scholar 

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Campos, L.M., Gámez, J.A., Larrañaga, P., Moral, S., Romero, T. (2002). Partial Abductive Inference in Bayesian Networks: An Empirical Comparison Between GAs and EDAs. In: Larrañaga, P., Lozano, J.A. (eds) Estimation of Distribution Algorithms. Genetic Algorithms and Evolutionary Computation, vol 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1539-5_16

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  • DOI: https://doi.org/10.1007/978-1-4615-1539-5_16

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-5604-2

  • Online ISBN: 978-1-4615-1539-5

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