A. A. Sirota, E. Yu. Mitrofanova

Possibilities of creation optimal in a class of the linear estimations of casual processes and fields on the basis of implementation of procedures of direct and indirect training of two-layer neural networks on set of implementations statistically the bound input and output casual vectors are considered. Theoretical substantiations of convergence of weight factors of a two-layer linear neural network with the reduced number of neurons in the latent layer to components of the latent vectors received at the decision of the generalized task on own values are received. It is shown that on an output of a neural network approach of an optimal linear estimation of an input casual vector in the form of expansion under the first latent vectors of a matrix of a covariance of the estimation which number is equal to number of neurons in the latent layer is formed. Possibilities of creation optimal in a class of the linear estimations of vectors of unobservable parameters are considered at indirect training of two-layer neural networks on set of implementations of observable casual vectors. It is shown that at adjustment of coefficients of a neural network in the conditions of indirect training under the observable data in the latent layer it is possible to receive an optimal estimation of a vector of unobservable parameters. Results of statistical simulation modeling on an example of handling of casual fields with a correlation given function are resulted.