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On the Capacity of Families of Characteristic Functions That Ensure Diagnostic Problems Are Solved Correctly

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Abstract

The capabilities and tools for quality evaluation of the results of intelligent data analysis (IDA) in problems of a diagnostic type are discussed. The reliability (indisputability) of the empirical dependencies formed during machine learning (interpolation-extrapolation) by precedents is evaluated by means of special logical tools, viz. characteristic functions. To generate characteristic functions using the available sample of precedents, the similarity of precedent descriptions, formalized as a binary algebraic operations, is analyzed. A method for evaluating the representativeness of the initial training sample is proposed to ensure that diagnostic problems are correctly solved. This method leverages a procedural scheme that reconstructs what causes diagnosable effects to arise and is implemented by the IDA tools in hand. The complexity of the computations associated with the application of the proposed mathematical toolset based on characteristic functions is estimated.

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Notes

  1. Given only the precedents listed in the respective sample.

  2. Operating with meaningful concepts of the subject domain involved.

  3. That is, satisfying the BCE condition, see above.

  4. Taking into account the respective closures—see above.

  5. Which allows an expert in the respective subject domain (because it is this expert rather than a computer system who makes the final decision) to match the results of the performed computer data analysis with his already accumulated professional experience and meaningful ideas on the nature of the effects being diagnosed.

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  1. Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, 119333, Moscow, Russia

    M. I. Zabezhailo

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  1. M. I. Zabezhailo
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Translated by M. Talacheva

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Zabezhailo, M.I. On the Capacity of Families of Characteristic Functions That Ensure Diagnostic Problems Are Solved Correctly. Sci. Tech. Inf. Proc. 49, 385–392 (2022). https://doi.org/10.3103/S0147688222050148

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