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Integrating integer programming and probabilistic deduction graphs for probabilistic reasoning

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Journal of Systems Integration

Abstract

Optimal solutions of several variants of the probabilistic reasoning problem were found by a new technique that integrates integer programming and probabilistic deduction graphs (PDG). PDGs are extended from deduction graphs of the and-type via normal deduction graphs. The foregoing variants to be solved can involve multiple hypotheses and multiple evidences where the former is given and the latter is unknown and being found or vice versa. The relationship among these hypotheses and evidences with possible intermediaries is represented by a causal graph. The proposed method can handle a large causal graph of any type and find an optimal solution by invoking a linear integer programming package. In addition, formulating the reasoning problem to fit integer programming takes a polynomial time.

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References

  1. J.B. Adams, “Probabilistic reasoning and certainty factors,”Math. Biosci., vol. 32, pp. 177–186, 1976; also in: [2], pp. 263–272.

    MATH  Google Scholar 

  2. B.G. Buchanan and E.H. Shortliffe, eds.,Rule-Based Expert Systems: The MYCIN Experiments of the Stanford Heuristic Programming Project, Addison-Wesley: Reading, MA, 1984.

    Google Scholar 

  3. E. Charniak and D. McDermott,Introduction to Artificial Intelligence, Addison-Wesley: Reading, MA, 1987, pp. 453–482.

    Google Scholar 

  4. P. Cohen, J. Delisio, M. Greenberg, R. Kjeldsen, D. Suthers, and P. Berman, “Management of uncertainty in medicine,”Int. J. of Approximate Reasoning, vol. 1, no. 1, pp. 103–116, 1987.

    Article  Google Scholar 

  5. J. Gordon and E.H. Shortliffe, “A method for managing evidential reasoning in a hierarchical hypothesis space,”Artificial Intelligence, vol. 26, no. 3, pp. 323–357, 1985.

    Article  MathSciNet  Google Scholar 

  6. D. Heckerman, “Probabilistic interpretations for MYCIN's certainty factors,” in [9], pp. 167–195.

    Google Scholar 

  7. W.B. Horng and C.C. Yang, “A shortest path algorithm to find minimal deduction graphs,”Data and Knowledge Eng., vol. 6, pp. 27–46, 1991.

    Article  Google Scholar 

  8. E. Horvitz and D. Heckerman, “The inconsistent use of measures of certainty in artificial intelligence research,” in [9], pp. 137–151.

    Google Scholar 

  9. L.N. Kanal and J.F. Lemmer, eds.,Uncertainty in Artificial Intelligence, North Holland: New York, 1986.

    Google Scholar 

  10. H.-L. Li and C.C. Yang, “Abductive reasoning by constructing probabilistic deduction graphs for solving the diagnosis problem,” Decision Support Systems, pp. 121–131, 1991.

  11. J. Pearl, “Fusion, propagation, and structuring in belief networks,”Artificial Intelligence, vol. 29, no. 3, pp. 241–288, 1986.

    Article  MATH  MathSciNet  Google Scholar 

  12. J. Pearl, “Embracing causality in formal reasoning,”Artificial Intelligence, vol. 35, no. 2, pp. 259–271, 1988.

    Article  MathSciNet  Google Scholar 

  13. J. Pearl,Probabilistic Reasoning in Intelligent Systems, Morgan-Kaufmann: San Mateo, CA, 1988.

    Google Scholar 

  14. H. Pople, “Heuristic methods for imposing structure on ill-structured problems: The structuring medical diagnosis,” in P. Szolovits, ed.,Artificial Intelligence in Medicine, Westview Press: Boulder, CO 1982, pp. 119–185.

    Google Scholar 

  15. L. Schrage,Users Manual for Linear, Integer, and Quadratic Programming with LINDO, The Scientific Press: Palo Alto, CA, 1985.

    Google Scholar 

  16. G. Shafer and R. Logan, “Implementing Dempster's rule for hierarchical evidence,”Artificial Intelligence, vol. 33, no. 3, pp. 271–298, November 1987.

    Article  MathSciNet  Google Scholar 

  17. H.A. Taha,Integer Programming, Academic Press: New York, 1975, pp. 116–119.

    Google Scholar 

  18. C.C. Yang, “A polynomial algorithm for logically deducing Horn clauses and processing queries,”Int. J. Pattern Recognition and Artificial Intelligence, vol. 1, no. 1, pp. 157–168, April 1987.

    Article  Google Scholar 

  19. C.C. Yang, “Deduction graphs: An algorithm and applications,”IEEE Trans. Software Eng., vol. 15, no. 1, pp. 60–67, January 1989.

    Article  MATH  Google Scholar 

  20. C.C. Yang, J.J.Y. Chen, and H.L. Chau, “Algorithms for constructing minimal deduction graphs,”IEEE Trans. Software Eng., vol. 15, no. 6 pp. 760–770, June 1989.

    Article  Google Scholar 

  21. J. Yen, “Gertis: A Dempster-Shafer approach to diagnosing hierarchical hypotheses,”Comm. ACM, vol. 32, no. 5 pp. 573–585, 1989.

    Article  Google Scholar 

  22. L.A. Zadeh, “The role of fuzzy sets in the management of uncertainty in expert systems,” in M. Gupta and B.K. Kandel, eds.,Approximate Reasoning in Expert Systems, North Holland: New York, 1985, pp. 3–31.

    Google Scholar 

  23. L.A. Zadeh, “A simple view of the Dempster-Shafer theory of evidence and its application for the rule of combination,”AI Machine, vol. 7, pp. 85–90, 1986.

    Google Scholar 

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H.-L. Li was visiting the Department of Computer Sciences, University of North Texas in 1988–1989. He is with the Institute of Information Management, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.

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Li, HL., Yang, CC. Integrating integer programming and probabilistic deduction graphs for probabilistic reasoning. Journal of Systems Integration 1, 195–214 (1991). https://doi.org/10.1007/BF02426923

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  • DOI: https://doi.org/10.1007/BF02426923

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