Deep data density estimation through Donsker-Varadhan representation

Abstract

Estimating the data density is one of the challenging problem topics in the deep learning society. In this paper, we present a simple yet effective methodology for estimating the data density using the Donsker-Varadhan variational lower bound on the KL divergence and the modeling based on the deep neural network. We demonstrate 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. Also, we present the deep neural network-based modeling and its stochastic learning procedure. The experimental results and possible applications of the proposed method demonstrate that it is competitive with the previous methods for data density estimation and has a lot of possibilities for various applications.