  Estimating the data density is one of the challenging problems in deep
learning. In this paper, we present a simple yet effective method for
estimating the data density using a deep neural network and the
Donsker-Varadhan variational lower bound on the KL divergence. We show that the
optimal critic function associated with the Donsker-Varadhan representation on
the KL divergence between the data and the uniform distribution can estimate
the data density. We also present the deep neural network-based modeling and
its stochastic learning. The experimental results and possible applications of
the proposed method demonstrate that it is competitive with the previous
methods and has a lot of possibilities in applied to various applications.
