Recognition of small samples with a given data distribution
using artificial neurons that predict the confidence probabilities of their own decisions 

Vladimir I. Volchikhin, Doctor of engineering sciences, professor, president of Penza State University (40 Krasnaya street, Penza, Russia), E-mail: cnit@pnzgu.ru
Aleksandr I. Ivanov, Doctor of engineering sciences, professor, scientific adviser, Penza Scientific Research Electrotechnical Institute (9 Sovetskaya street, Penza, Russia), E-mail: ivan@pniei.penza.ru
Aleksandr V. Bezyaev, Candidate of engineering sciences, doctor’s degree student, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: tsib@pnzgu.ru
Ivan A. Filipov, Lecturer, Military Training Center, Penza State University (40 Krasnaya street, Penza, Russia), E-mail: re.wo1f@mail.ru 

Background. Improving the reliability of statistical data processing on small samples. Materials and methods - it is proposed to use three artificial neurons, which are analogues of the chi-square test, the fourth statistical moment test and the Geary test. Additionally, the procedure for additional training of output nonlinear functions of artificial neurons was used to predict the confidence probabilities regarding decisions made by neurons. Results. A significant increase in the number of detected and corrected errors during the convolution of redundant codes of the neural network classifier is shown. Conclusions. It has been confirmed that the use of several statistical criteria in parallel gives a more reliable result in comparison with one criterion, and complex code designs capable of detecting and correcting errors can be used to combine them. A numerical experiment confirmed that a two-layer neural network can reduce the level of detected, but not correctable, errors to a probability of 0.141. Linear extrapolation of the results of a numerical experiment allows us to expect a confidence probability of 0.9 already when using 5 artificial neurons of the first layer. Thus, there is a significant reduction in the cost of protecting applications due to the use of SIM cards, RFID cards, microSD cards, USB BioTokens, FPGAs, DSP controllers in a trusted computing environment. 

chi-square test, fourth statistical moment test, Geary's test, small samples, testing of the normality hypothesis 

Volchikhin V.I., Ivanov A.I., Bezyaev A.V., Filipov I.A. Recognition of small samples with a given data distribution using artificial neurons that predict the confidence probabilities of their own decisions. Izvestiya vysshikh uchebnykh zavedeniy. Povolzhskiy region. Tekhnicheskie nauki = University proceedings. Volga region. Engineering sciences. 2023;(4):31–39. (In Russ.). doi: 10.21685/2072-3059-2023-4-3