Abstract
Generative adversarial nets (GANs) and variational
auto-encoders have significantly improved our distribution
modeling capabilities, showing promise for dataset augmentation, image-to-image translation and feature learning. However, to model high-dimensional distributions, sequential training and stacked architectures are common, increasing the number of tunable hyper-parameters as well as
the training time. Nonetheless, the sample complexity of the
distance metrics remains one of the factors affecting GAN
training. We first show that the recently proposed sliced
Wasserstein distance has compelling sample complexity
properties when compared to the Wasserstein distance. To
further improve the sliced Wasserstein distance we then analyze its ‘projection complexity’ and develop the max-sliced
Wasserstein distance which enjoys compelling sample complexity while reducing projection complexity, albeit necessitating a max estimation. We finally illustrate that the proposed distance trains GANs on high-dimensional images up
to a resolution of 256x256 easily.