Generative adversarial networks constitute a powerful approach to generative modeling. While generated samples often are indistinguishable from real data, 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：生成对抗网络为生成建模提供了一种强有力的方法。尽管生成样本往往与真实数据难以区分，但并不能保证它们遵循真实的数据分布。特别是在科学应用中，生成分布能否准确捕捉真实分布至关重要。本文提出一种方法，确保特定生成数据统计量的分布与真实数据的对应分布保持一致。为实现这一目标，我们在生成器损失函数中引入新的损失项，通过适当的f-散度量化这些分布间的差异。采用核密度估计方法获取真实分布的表示，并在每次迭代中根据小批量数据估计相应的生成分布。与其他方法相比，本方法的优势在于全面考虑了分布的整体形态。我们在合成数据集和真实数据集上对该方法进行评估，并证明了其性能提升。