Estimating the Probability of a Class at a Point by the Approximation of One Discriminant Function
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.
Keywordsmachine learning classification evaluating posterior probability of a class approximation of a discriminant function disease diagnostics
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- 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
- 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.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.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.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
- 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.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.Problem at TMSh 2014. http://www.machinelearning.ru/wiki/images/e/e1/School-VI-2014-task-3.rar