We propose a novel deep generative model, the Kolmogorov-Smirnov Generative Adversarial Network (KSGAN). Unlike existing approaches, KSGAN formulates the learning process as a minimization of the Kolmogorov-Smirnov (KS) distance, generalized to handle multivariate distributions. This distance is calculated using the quantile function, which acts as the critic in the adversarial training process. We formally demonstrate that minimizing the KS distance leads to the trained approximate distribution aligning with the target distribution. We propose an efficient implementation and evaluate its effectiveness through experiments. The results show that KSGAN performs on par with existing adversarial methods, exhibiting stability during training, resistance to mode dropping and collapse, and tolerance to variations in hyperparameter settings. Additionally, we review the literature on the Generalized KS test and discuss the connections between KSGAN and existing adversarial generative models.

我们提出了一种新颖的深层生成模型，Kolmogorov-Smirnov生成对抗网络（KSGAN）。与现有方法不同，KSGAN将学习过程规范为最小化Kolmogorov-Smirnov（KS）距离，该距离被推广用于处理多变量分布。我们正式证明最小化KS距离会导致训练得到的近似分布与目标分布对齐。我们提出了一种高效的实现方法，并通过实验评估其有效性。结果表明，KSGAN性能与现有对抗性方法相当，在训练过程中表现稳定，具有防止模式消失和崩溃的能力，并且对超参数设置变化具有容差性。此外，我们回顾了关于广义KS检验的文献，并讨论了KSGAN与现有对抗生成模型之间的关系。

Kolmogorov-Smirnov GAN