Neural network analysis of small samples using a large number of statistical criteria to test the sequence of hypotheses about the value of mathematical expectations of correlation coefficients
Background. The purpose of the article is to improve the accuracy of neural network estimates of correlation coefficients. Materials and methods. The correlation coefficient is one of the most significant second-order statistical points. When training networks of quadratic neurons on small sample...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Penza State University Publishing House
2024-11-01
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| Series: | Известия высших учебных заведений. Поволжский регион:Технические науки |
| Subjects: | |
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| Summary: | Background. The purpose of the article is to improve the accuracy of neural
network estimates of correlation coefficients. Materials and methods. The correlation
coefficient is one of the most significant second-order statistical points. When training
networks of quadratic neurons on small samples, it is necessary to repeatedly reduce the
probabilities of errors of the first and second kinds, classical statistical criteria. Previously,
it was shown that the representation of various statistical criteria by artificial neurons leads
to the emergence of some equivalent of convolutional neural networks, which increase the
accuracy of estimating correlation coefficients. Results. The networks increase the accuracy
of estimates of correlation coefficients when testing the sequence of different statistical
hypotheses with a second layer, which eliminates the code redundancy of a large number of
neurons of the first layer. The number of hypotheses to be tested must coincide with the
number of output states of convolutional artificial neurons. The paper discusses artificial
convolutional neurons with output quantizers having 8 quantization thresholds with
mathematical expectations E(r) ≈ {0.0; ±0.3; ±0.5; ±0.7; ±0.9} correlation coefficients. |
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| ISSN: | 2072-3059 |