Generative adversarial networks constitute a powerful approach to generative modeling. While generated samples often are indistinguishable from real data, mode-collapse may occur and there is no guarantee that they will follow the true data distribution. For scientific applications in particular, it is essential that the true distribution is well captured by the generated distribution. In this work, we propose a method to ensure that the distributions of certain generated data statistics coincide with the respective distributions of the real data. In order to achieve this, we add a new loss term to the generator loss function, which quantifies the difference between these distributions via suitable f-divergences. Kernel density estimation is employed to obtain representations of the true distributions, and to estimate the corresponding generated distributions from minibatch values at each iteration. When compared to other methods, our approach has the advantage that the complete shapes of the distributions are taken into account. We evaluate the method on a synthetic dataset and a real-world dataset and demonstrate improved performance of our approach.

翻译：生成对抗网络构成了生成建模的有力方法。尽管生成的样本通常与真实数据难以区分，但可能出现模式崩溃，且无法保证其遵循真实数据分布。尤其在科学应用中，确保真实分布被生成分布充分捕捉至关重要。本研究提出一种方法，确保特定生成数据统计量的分布与真实数据的相应分布一致。为实现这一目标，我们在生成器损失函数中新增一项损失项，通过合适的f-散度量化这些分布之间的差异。采用核密度估计获得真实分布的表示，并在每次迭代中通过小批量值估计对应生成分布。与其他方法相比，我们的方法优势在于考虑了分布的完整形状。我们在合成数据集和真实数据集上评估了该方法，并展示了其性能提升。