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On statistical classification problems with error constraints

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Cybernetics Aims and scope

Conclusions

Our main results may be summarized as follows. The statistical problem of multialternative classification under constraints is stated as a problem of linear programming in functional space.

Necessary and sufficient conditions are obtained for the existence of an optimal decision, in the form of a functional analog of the Kuhn-Tucker theorem, yielding a system of equations and inequalities for finding the optimal decision rules.

The structure of the optimal rules is obtained for two types of functional and six types of constraint, which are given a meaningful treatment in the context of medical diagnosis problems.

Sufficient conditions for the optimal rules to be unrandomized are obtained in some particular cases.

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Authors
  1. O. Yu. Kul'chitskii
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  2. A. V. Sloushch
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  3. Yu. V. Sokolov
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Additional information

Translated from Kibernetika, No. 2, pp. 83–91, March–April, 1981.

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Kul'chitskii, O.Y., Sloushch, A.V. & Sokolov, Y.V. On statistical classification problems with error constraints. Cybern Syst Anal 17, 248–258 (1981). https://doi.org/10.1007/BF01069642

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  • DOI: https://doi.org/10.1007/BF01069642

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