Method for operating neural network and system for learning stochastic inference models

A system and method for operating a neural network. In some embodiments, the neural network includes a variational autoencoder, and the training of the neural network includes training the variational autoencoder with a plurality of samples of a first random variable; and a plurality of samples of a second random variable, the plurality of samples of the first random variable and the plurality of samples of the second random variable being unpaired, the training of the neural network including updating weights in the neural network based on a first loss function, the first loss function being based on a measure of deviation from consistency between: a conditional generation path from the first random variable to the second random variable, and a conditional generation path from the second random variable to the first random variable.