Concurrent Density Estimation with Wasserstein Autoencoders: Some
  Statistical Insights
Anish Chakrabarty Arkaprabha Basu Swagatam Das
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.