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

TL;DR

This paper introduces the Empirical Beta Copula Autoencoder, a new nonparametric method for modeling latent spaces in autoencoders to enable effective data generation, comparing it with existing techniques.

Contribution

The paper proposes a novel copula-based approach for modeling autoencoder latent spaces, enhancing simplicity and flexibility in generative modeling.

Findings

Empirical Beta Copula Autoencoder performs competitively with existing methods.

Copula-based models offer advantages in capturing complex dependencies.

Insights into targeted sampling and feature-specific data synthesis are provided.

Abstract

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.