Sets of autoencoders with shared latent spaces

Autoencoders receive latent models of input data. It was shown in recent works that they also estimate probability density functions of the input. This fact makes using the Bayesian decision theory possible. If we obtain latent models of input data for each class or for some points in the space of parameters in a parameter estimation task, we are able to estimate likelihood functions for those classes or points in parameter space. We show how the set of autoencoders solves the recognition problem. Each autoencoder describes its own model or context, a latent vector that presents input data in the latent space may be called treatment in its context. Sharing latent spaces of autoencoders gives a very important property that is the ability to separate treatment and context where the input information is treated through the set of autoencoders. There are two remarkable and most valuable results of this work: a mechanism that shows a possible way of forming abstract concepts and a way of reducing dataset's size during training. These results are confirmed by tests presented in the article.