Learning Nonparametric High-Dimensional Generative Models: The
  Empirical-Beta-Copula Autoencoder
Maximilian Coblenz Oliver Grothe Fabian Kächele
By sampling from the latent space of an autoencoder and decoding the latent
space samples to the original data space, any autoencoder can simply be turned
into a generative model. For this to work, it is necessary to model the
autoencoder's latent space with a distribution from which samples can be
obtained. Several simple possibilities (kernel density estimates, Gaussian
distribution) and more sophisticated ones (Gaussian mixture models, copula
models, normalization flows) can be thought of and have been tried recently.
This study aims to discuss, assess, and compare various techniques that can be
used to capture the latent space so that an autoencoder can become a generative
model while striving for simplicity. Among them, a new copula-based method, the
Empirical Beta Copula Autoencoder, is considered. Furthermore, we provide
insights into further aspects of these methods, such as targeted sampling or
synthesizing new data with specific features.