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By sampling from the latent space of an autoencoder and decoding the latentspace samples to the original data space, any autoencoder can simply be turnedinto a generative model. For this to work, it is necessary to model theautoencoder's latent space with a distribution from which samples can beobtained. Several simple possibilities (kernel density estimates, Gaussiandistribution) and more sophisticated ones (Gaussian mixture models, copulamodels, normalization flows) can be thought of and have been tried recently.This study aims to discuss, assess, and compare various techniques that can beused to capture the latent space so that an autoencoder can become a generativemodel while striving for simplicity. Among them, a new copula-based method, theEmpirical Beta Copula Autoencoder, is considered. Furthermore, we provideinsights into further aspects of these methods, such as targeted sampling orsynthesizing new data with specific features.

Learning Nonparametric High-Dimensional Generative Models: The Empirical-Beta-Copula Autoencoder