Annals of Operations Research

, Volume 21, Issue 1, pp 1–29 | Cite as

Heuristic least-cost computation of discrete classification functions with uncertain argument values

  • Louis Anthony COXJr.
  • Yuping QIU
  • Warren Kuehner
Article

Abstract

We consider the problem of minimizing the expected cost of computing the correct value of a discrete-valued function when it is costly to determine (“inspect”) the values of its arguments. This type of problem arises in distributed computing, in the design of interactive expert systems, in reliability analysis of coherent systems, in classification of pattern vectors, and in many other applications. In this paper, we first show that the general problem is NP-hard and then introduce several efficient heuristic sequential inspection procedures for solving it approximately. We obtain theoretical results showing that the heuristics are optimal in important special cases; moreover, their computational structures make them well suited for parallel implementation. Next, for the special case of linear threshold (or “discrete linear discriminant”) functions, which are widely used in statistical classification procedures, we use Monte Carlo simulation to analyze the performances of the heuristics and to compare the heuristic solutions with the exact (true minimum expected cost) solutions over a wide range of randomly generated test problems. All of the heuristics give average relative errors, compared to the exact optimal solutions, of less than 2%. The best heuristic for this class of functions gives an average relative error of less than 0.05% and runs two to four orders of magnitude faster than the exact solution procedure, for functions with ten arguments.

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References

  1. [1]
    M.O. Ball and J.S. Provan, Disjoint products and efficient computation of relability, Operations Research 36, No. 5 (1988) 703–715.Google Scholar
  2. [2]
    Y. Ben-Dov, A branch and bound algorithm for minimizing the expected cost of testing coherent system, European Journal of Operational Research 7 (1981) 284–289.Google Scholar
  3. [3]
    Y. Ben-Dov, Optimal testing procedures for special structures of coherent system, Management Science 27, No. 12 (December 1981) 1410–1420.Google Scholar
  4. [4]
    L. Breiman, J. Friedman, R. Olshen and C. Stone,Classification and Regression Trees (Wadsworth, Belmont, CA, 1984).Google Scholar
  5. [5]
    R.W. Butterworth, Some reliability fault-testing models, Operations Research 20 (1972) 335–343.Google Scholar
  6. [6]
    C.J. Colbourn,The Combinatorics of Network Reliability (Oxford University Press, New York, 1987).Google Scholar
  7. [7]
    L.A. Cox, Jr., Designing interactive expert classification systems that acquire expensive information ‘optimally’, in:Proc. European Knowledge Acquisition Workshop for Knowledge-Based Systems, eds. J. Boose et al. (Gesellschaft fur Mathematik und Datenverarbeitung MBH, GMD Studien Nr. 143, Bonn, Germany, 1988).Google Scholar
  8. [8]
    M.R. Garey and D.S. Johnson,Computers and Intractability: A Guide to the Theory of NP-Completeness (W.H. Freeman, San Francisco, 1979).Google Scholar
  9. [9]
    J. Halpern, Fault-testing of ak-out-of-n system, Operations Research 22 (1974) 1267–1271.Google Scholar
  10. [10]
    J.N. Hooker, A quantitative approach to logical inference, Decision Support Systems 4 (1988) 45–69.Google Scholar
  11. [11]
    J.R. Quinlan, The effect of noise on concept learning, in:Machine Learning: An Artificial Intelligence Approach, eds. R.S. Michalski et al. (Morgan Kaufmann, Los Altos, CA, 1986).Google Scholar
  12. [12]
    C.L. Sheng,Threshold Logic (Academic Press, New York, 1969).Google Scholar
  13. [13]
    R.E. Tarjan, A unified approach to path problems, Journal of the ACM 28 (1981) 577–593.Google Scholar
  14. [14]
    S. Tsukiyama, I. Shirakawa, H. Ozaki and H. Ariyoshi, An algorithm to enumerate all cutsets of a graph in linear time per cutset, Journal of the ACM 27 (1980) 619–632.Google Scholar
  15. [15]
    J.D. Ullman,Principles of Database Systems, 2nd Ed. (Computer Science Press, Rockville, Md. 1982).Google Scholar

Copyright information

© J.C. Baltzer A.G. Scientific Publishing Company 1989

Authors and Affiliations

  • Louis Anthony COXJr.
    • 1
  • Yuping QIU
    • 1
  • Warren Kuehner
    • 1
  1. 1.Department of Science and TechnologyUS WEST Advanced TechnologiesEnglewoodUSA

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