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

Abstract

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.

Keywords

• correlation coefficients
• small samples
• statistical criteria for testing the independence hypothesis
• artificial neurons
• improving the accuracy of estimates by eliminating code redundancy