Assessing distance betweeen the true and the sample distribution is a key component of many state of the art generative models, such as Wasserstein Autoencoder (WAE). Inspired by prior work on Sliced-Wasserstein Autoencoders (SWAE) and
 kernel smoothing we construct a new generative model – Cramer-Wold AutoEncoder (CWAE). CWAE cost function, based on introduced Cramer-Wold distance between samples, has a simple closed-form in the case of normal prior. As a consequence, while simplifying the optimization procedure (no need of sampling necessary to evaluate the distance function in the training loop), CWAE performance matches quantitatively and qualitatively that of WAE-MMD (WAE using maximum mean discrepancy based distance function) and often improves upon SWAE.
Inspired by prior work on Sliced-Wasserstein Autoencoders (SWAE) and kernel smoothing we construct a new generative model – Cramer-Wold AutoEncoder (CWAE). This paper proposes a WAE variant based on a new statistical distance between the encoded data distribution and the latent prior distribution Introduces a variation on the Wasserstein AudoEncoders which is a novel regularized auto-encoder architecture that proposes a specific choice of the divergence penalty This paper proposes the Cramer-Wold autoencoder, which uses the Cramer-Wold distance between two distributions based on the Cramer-Wold Theorem.