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Automation and Remote Control

, Volume 79, Issue 9, pp 1582–1592 | Cite as

Estimating the Probability of a Class at a Point by the Approximation of One Discriminant Function

  • V. V. Zenkov
Stochastic Systems
  • 2 Downloads

Abstract

We propose a method for estimating the posterior probability of a class at a given point by approximating a discriminant function that takes a zero value at this point. The approximation is based on a supervised training set. Posterior probabilities of classes allow the classification problem to be solved simultaneously for different criteria and different costs of classification errors. The method is based on choosing such a ratio of the costs of classification errors in the construction of an approximation to the discriminant function that the approximation takes the zero value at a given point. We give a model example and an example with real data from the field of medical diagnostics.

Keywords

machine learning classification evaluating posterior probability of a class approximation of a discriminant function disease diagnostics 

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References

  1. 1.
    Anderson, T.W., An Introduction to Multivariate Statistical Analysis, New York: Wiley, 2003, 3rd ed.zbMATHGoogle Scholar
  2. 2.
    Tsypkin, Ya.Z. and Kel’mans, G.K., Adaptive Bayesian Approach, Probl. Peredachi Inform., 1970, vol. 6, no. 1, pp. 52–59.MathSciNetGoogle Scholar
  3. 3.
    Zenkov, V.V., Approximating Discriminant Functions in the Neighborhood of Zero Values, Izv. Ross. Akad. Nauk, Tekh. Kibern., 1973, no. 2, pp. 152–156.Google Scholar
  4. 4.
    Zenkov, V.V., Using Weighted Least Squares to Approximate the Discriminant Function with a Cylindrical Surface in Classification Problems, Autom. Remote Control, 2017, vol. 78, no. 9, pp. 1662–1673.MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Hastie, T., Tibshirani, R., and Friedman, J., The Elements of Statistical Learning: Data Mining, Inference, and Prediction, Berlin: Springer, 2009, 2nd ed.CrossRefzbMATHGoogle Scholar
  6. 6.
    Niculescu-Mizil, A. and Caruana, R., Predicting Good Probabilities with Supervised Learning, Proc. 22nd Int. Conf. on Machine Learning, ICML’05, Bonn, Germany, August 7–11, 2005, pp. 625–632. http://www.cs.cornell.edu/~alexn/papers/calibration.icml05.crc.rev3.pdf Google Scholar
  7. 7.
    Bella, A., Ferri, C., Hernández-Orallo, J., and Ramírez-Quintana, M., Calibration of Machine Learning Models, in Handbook of Research on Machine Learning Applications and Trends: Algorithms, Methods, and Techniques, Hershey: IDI, 2010, pp. 19. http://users.dsic.upv.es/~flip/papers/BFHRHandbook2010.pdf Google Scholar
  8. 8.
    Zenkov, V.V., Machine Learning. A Method of Approximation of Discriminant Functions and Two Methods of Estimation of Posterior Probabilities of Classes in the Problem of Classification, Proc. 10th Int. Conf. “Management of Large-Scale System Development” (MLSD’2017, 2–4 Oct. 2017), IEEE Conf, pp. 1–4. http://ieeexplore.ieee.org/document/8109715/ Google Scholar
  9. 9.
    Vorontsov, K.V., Matematicheskie metody obucheniya po pretsedentam (teoriya obucheniya mashin) (Mathematical Methods of Precedent Learning (Machine Learning Theory)). http://www.machinelearning.ru/wiki/images/6/6d/Voron-ML-1.pdf
  10. 10.
    Merkov, A.B., Raspoznavanie obrazov. Vvedenie v metody statisticheskogo obucheniya (Pattern Recognition. Introduction to Statistical Learning), Moscow: URSS, 2011. http://www.recognition.mccme.ru/pub/RecognitionLab.html/slbook.pdfGoogle Scholar
  11. 11.
    Anufriev, I.E., Smirnov, A.B., and Smirnova, E.N., MATLAB 7, St. Petersburg: BKhV-Peterburg, 2005. http://fileskachat.com/file/31353 4197b1d0a54318bac8271e5daca525b0.htmlGoogle Scholar
  12. 12.
    Zenkov, V.V., Software for Constructing an Approximation of a Discriminant Function by a Training Sample with Higher Accuracy in the Neighborhood of Zero Values, Software Registration Certificate no. 2017660808, 2017.Google Scholar
  13. 13.
    Zenkov, V.V., Estimating the Posterior Probability of a Class at a Point by an Approximation of One Discriminant Function, Software Registration Certificate no. 2017660807, 2017.Google Scholar
  14. 14.

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Trapeznikov Institute of Control SciencesRussian Academy of SciencesMoscowRussia

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