Concurrent Density Estimation with Wasserstein Autoencoders: Some Statistical Insights
This work offers incremental theoretical insights into WAEs, benefiting researchers in deep generative models by enhancing understanding of model resilience and statistical properties.
The paper tackles the problem of providing a theoretical understanding of Wasserstein Autoencoders (WAEs) by framing it as concurrent density estimation tasks, establishing deterministic upper bounds on errors and analyzing error propagation under adversarial conditions.
Variational Autoencoders (VAEs) have been a pioneering force in the realm of deep generative models. Amongst its legions of progenies, Wasserstein Autoencoders (WAEs) stand out in particular due to the dual offering of heightened generative quality and a strong theoretical backbone. WAEs consist of an encoding and a decoding network forming a bottleneck with the prime objective of generating new samples resembling the ones it was catered to. In the process, they aim to achieve a target latent representation of the encoded data. Our work is an attempt to offer a theoretical understanding of the machinery behind WAEs. From a statistical viewpoint, we pose the problem as concurrent density estimation tasks based on neural network-induced transformations. This allows us to establish deterministic upper bounds on the realized errors WAEs commit. We also analyze the propagation of these stochastic errors in the presence of adversaries. As a result, both the large sample properties of the reconstructed distribution and the resilience of WAE models are explored.