Abstract
Belief networks encode joint probability distribution functions and can be used as fitness functions in genetic algorithms. Individuals in the genetic algorithm's population then represent instantiations, or explanations, in the belief network. Computing the most probable explanations (belief revision) is thus cast as a genetic algorithm search in the joint probability distribution space. At any time, the best fit individual in the genetic algorithm population is an estimate of the most probable explanation. This paper argues that joint probability distribution functions represented by belief networks typically are multimodal and highly variable. Thus the genetic algorithm techniques known as sharing and scaling should be of help. It is shown empirically that this is indeed the case, in particular that niching combined with scaling significantly improves the quality of a genetic algorithm's estimate of the most probable explanations. A novel scaling approach, root scaling, is also introduced.
This work was supported in part by ONR Grant N00014-95-1-0749, ARL Grant DAAL01-96-2-0003, and NRL Grant N00014-97-C-2061. Thanks also go to David E. Goldberg for comments on and discussions related to previous versions of this paper. Comments from reviewers are also acknowledged.
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J. E. Baker. Reducing bias and inefficiency in the selection algorithm. In Grefenstette [9], pages 14–21.
P. Darwen and X. Yao. Every niching method has its niche: Fitness sharing and implicit sharing compared. In Proc. Parallel Problem Solving from Nature — PPSN IV, pages 398–407, New York, NY, 1996. Springer.
K. A. De Jong and W. M. Spears. Using genetic algorithms to solve NP-complete problems. In J. D. Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, San Mateo, CA, 1989. Morgan Kaufman.
K. Deb and D. E. Goldberg. An investigation of niche and species-formation in genetic function optimization. In J. D. Schaffer, editor, Proceedings of the Third International Conference on Genetic Algorithms, San Mateo, CA, 1989. Morgan Kaufman.
E. S. Gelsema. Abductive reasoning in Bayesian belief networks using a genetic algorithm. Pattern Recognition Letters, 16:865–871, 1995.
D. E. Goldberg. Genetic Algorithms in Search, Optimization & Machine Learning. Addison-Wesley, Reading, MA, 1989.
D. E. Goldberg, K. Deb, and J. Horn. Massive multimodality, deception, and genetic algorithms. Technical Report IlliGAL Report No 92005, University of Illinois, Urbana, 1992.
D. E. Goldberg and J. Richardson. Genetic algorithms with sharing for multimodal function optimization. In Grefenstette [9], pages 41–49.
J. J. Grefenstette, editor. Proceedings of the Second International Conference on Genetic Algorithms, Hillsdale, New Jersey, 28–31 July 1987. Lawrence Erlbaum Associates.
R. Lin, A. Galper, and R. Shachter. Abductive inference using probabilistic networks: Randomized search techniques. Technical Report KSL-90-73, Knowledge Systems Laboratory, Stanford, November 1990.
O. J. Mengshoel. Belief network inference in dynamic environments. In Proc. of AAAI-97, page 813, Providence, RI, 1997.
O. J. Mengshoel, D. E. Goldberg, and D. C. Wilkins. Deceptive and other functions of unitation as Bayesian networks. In Genetic Programming 1998: Proceedings of the Third Annual Conference, Madison, WI, July 1998. To appear.
O. J. Mengshoel and D. C. Wilkins. Abstraction for belief revision: Using a genetic algorithm to compute the most probable explanation. In Proc. 1998 AAAI Spring Symposium on Satisficing Models, pages 46–53, Stanford University, CA, March 1998.
J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann, San Mateo, California, 1988.
C. Rojas-Guzman and M. A. Kramer. An evolutionary computing approach to probabilistic reasoning on Bayesian networks. Evolutionary Computation, 4(1):57–85, 1996.
E. Shimony. Finding MAPs for belief networks is NP-hard. Artificial Intelligence, 68:399–410, 1994.
S. Srinivas and J. Breese. IDEAL: A software package for analysis of influence diagrams. In Proceedings of the Sixth Conference on Uncertainty in Artificial Intelligence, pages 212–219, July 1990.
R. L. Welch. Real time estimation of Bayesian networks. In Proceedings of the Twelfth Annual Conference on Uncertainty in Artificial Intelligence (UAI-96), pages 533–544, Portland, Oregon, 1996.
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Mengshoel, O.J., Wilkins, D.C. (1998). Genetic algorithms for belief network inference: The role of scaling and niching. In: Porto, V.W., Saravanan, N., Waagen, D., Eiben, A.E. (eds) Evolutionary Programming VII. EP 1998. Lecture Notes in Computer Science, vol 1447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0040806
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DOI: https://doi.org/10.1007/BFb0040806
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