Cramer-Wold AutoEncoder
Abstract
We propose a new generative model, Cramer-Wold Autoencoder (CWAE). Following WAE, we directly encourage normality of the latent space. Our paper uses also the recent idea from Sliced WAE (SWAE) model, which uses one-dimensional projections as a method of verifying closeness of two distributions. The crucial new ingredient is the introduction of a new (Cramer-Wold) metric in the space of densities, which replaces the Wasserstein metric used in SWAE. We show that the Cramer-Wold metric between Gaussian mixtures is given by a simple analytic formula, which results in the removal of sampling necessary to estimate the cost function in WAE and SWAE models. As a consequence, while drastically simplifying the optimization procedure, CWAE produces samples of a matching perceptual quality to other SOTA models.
Keywords
Cite
@article{arxiv.1805.09235,
title = {Cramer-Wold AutoEncoder},
author = {Szymon Knop and Jacek Tabor and Przemysław Spurek and Igor Podolak and Marcin Mazur and Stanisław Jastrzębski},
journal= {arXiv preprint arXiv:1805.09235},
year = {2020}
}