Density estimation is one of the fundamental problems in both statistics and machine learning. In this study, we propose Roundtrip, a computational framework for general-purpose density estimation based on deep generative neural networks. Roundtrip retains the generative power of deep generative models, such as generative adversarial networks (GANs) while it also provides estimates of density values, thus supporting both data generation and density estimation. Unlike previous neural density estimators that put stringent conditions on the transformation from the latent space to the data space, Roundtrip enables the use of much more general mappings where target density is modeled by learning a manifold induced from a base density (e.g., Gaussian distribution). Roundtrip provides a statistical framework for GAN models where an explicit evaluation of density values is feasible. In numerical experiments, Roundtrip exceeds state-of-the-art performance in a diverse range of density estimation tasks.

密度估计是统计学和机器学习中的基本问题之一。在这项研究中，我们提出了 Roundtrip，这是一种基于深度生成神经网络的通用密度估计计算框架。Roundtrip 保留了深度生成模型的生成能力，例如生成对抗网络 (GAN)，同时它还提供密度值的估计，从而支持数据生成和密度估计。与之前的神经密度估计器对从潜在空间到数据空间的转换施加严格的条件不同，Roundtrip 允许使用更通用的映射，其中目标密度通过学习从基础密度（例如，高斯分布）诱导的流形来建模. Roundtrip 为 GAN 模型提供了一个统计框架，其中对密度值的明确评估是可行的。在数值实验中，Roundtrip 在各种密度估计任务中超过了最先进的性能。