Kolmogorov-Smirnov GAN

TL;DR

KSGAN introduces a new deep generative model that minimizes the Kolmogorov-Smirnov distance, using the quantile function as a critic, leading to stable training and good performance in generating complex distributions.

Contribution

The paper presents the first application of the KS distance in GANs, providing a novel formulation and demonstrating its effectiveness and stability compared to existing methods.

Findings

Performs on par with existing adversarial models

Exhibits stability during training

Resistant to mode dropping and collapse

Abstract

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.