The Use of Stochastic Parameter Identification in the Separation of Mixtures of Correlated Deep Gaussian Models

An important task in the processing of different types of data is to identify different internal patterns in these data, allowing you to identify hidden objects and areas, as well as to evaluate the parameters of these areas. To solve this problem, we propose to use deep Gaussian processes that make it possible to describe non-stationary multidimensional signals. Combining a sequence of deep Gaussian processes with Markov random fields makes it possible to describe multidimensional signals using the correlation relationships of a sequence element with its vicinity. The paper formulates the necessary mathematical apparatus for describing mixtures of correlated deep Gaussian models. To identify the parameters of such constructions it is proposed to use a modification of the Stochastic Expectation Maximization (SEM) algorithm. The necessary relations for the implementation of this approach are determined and the consistency of the method is shown.