Advertisement

The Rate of Convergence to the Limit of the Probability of Encountering an Accidental Similarity in the Presence of Counter Examples

  • D. V. Vinogradov
Information Analysis
  • 13 Downloads

Abstract

This paper refines the main result of [1], where the limit \( - {e^{ - a}} - a{e^{ - a}}\left[ {1 - {e^{ - c\sqrt a }}} \right]\) was proved for the probability of encountering an accidental similarity between two parent examples without \(m = c\sqrt n \) counter examples if each parent example and counter example is described by a series of \(\sqrt n \) independent Bernoulli trials with success probability \(p = \sqrt {a/n} \). In this paper, we prove that the rate of convergence to the limit is proportional to \({n^{\frac{1}{2}}}\).

Keywords

Bernoulli trials accidental similarity counter example 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Vinogradov, D.V., Asymptotic probability of encountering an accidental similarity in the presence of counter examples, Autom. Doc. Math. Linguist., 2017, vol. 51, no. 1, pp. 42–44.CrossRefGoogle Scholar
  2. 2.
    DSM-metod avtomaticheskogo porozhdeniya gipotez: Logicheskie i epistemologicheskie osnovaniya (The JSM Method of Automatic Hypothesis Generation: Logical and Epistemological Grounds), Finn, V.K. and Anshakov, O.M., Eds., Moscow: Editorial-URSS, 2009.Google Scholar
  3. 3.
    Ganter, B. and Wille, R., Formal Concept Analysis, Berlin: Springer-Verlag, 1999.CrossRefzbMATHGoogle Scholar
  4. 4.
    Vinogradov, D.V., VKF-method of hypotheses generation, Commun. Inf. Comput. Sci., 2014, vol. 436, pp. 237–248.Google Scholar
  5. 5.
    Vinogradov, D.V., The probability of encountering an accidental DSM similarity in the presence of counter examples, Autom. Doc. Math. Linguist., 2015, vol. 49, no. 2, pp. 43–46.CrossRefGoogle Scholar
  6. 6.
    Vinogradov, D.V., Accidental formal concepts in the presence of counterexamples, Proceedings of International Workshop on Formal Concepts Analysis for Knowledge Discovery (FCA4KD 2017): CEUR Workshop Proceedings, 2017, vol. 1921, pp. 104–112.Google Scholar

Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Federal Research Center Computer Science and ControlRussian Academy of SciencesMoscowRussia

Personalised recommendations