  Autoencoders and their variants are among the most widely used models in
representation learning and generative modeling. However, autoencoder-based
models usually assume that the learned representations are i.i.d. and fail to
capture the correlations between the data samples. To address this issue, we
propose a novel Sparse Gaussian Process Bayesian Autoencoder (SGPBAE) model in
which we impose fully Bayesian sparse Gaussian Process priors on the latent
space of a Bayesian Autoencoder. We perform posterior estimation for this model
via stochastic gradient Hamiltonian Monte Carlo. We evaluate our approach
qualitatively and quantitatively on a wide range of representation learning and
generative modeling tasks and show that our approach consistently outperforms
multiple alternatives relying on Variational Autoencoders.
