  We present the Incremental Generative Monte Carlo (IGMC) method, designed to
measure uncertainty in deep neural networks using deep generative approaches.
IGMC iteratively trains generative models, adding their output to the dataset,
to compute the posterior distribution of the expectation of a random variable.
We provide a theoretical guarantee of the convergence rate of IGMC relative to
the sample size and sampling depth. Due to its compatibility with deep
generative approaches, IGMC is adaptable to both neural network classification
and regression tasks. We empirically study the behavior of IGMC on the MNIST
digit classification task.
